tag:blogger.com,1999:blog-23316266225483978032024-03-13T04:18:34.351-07:00FinanMicrointerlabhttp://www.blogger.com/profile/13609644492940281686noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-2331626622548397803.post-61633625260333495372013-06-13T14:40:00.000-07:002020-03-10T22:30:10.637-07:00<span style="background-color: white;"><span style="background-color: white;"><span style="background-color: black;"></span></span></span><!--[if gte mso 9]><xml>
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<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Durante
mi experiencia como estudiante y en mi desempeño como profesional y con más de
8 años de experiencia asesorando a los microempresarios de los diversos
municipios del departamento, mediante capacitaciones, asesorías y conferencias,
pude darme cuenta de las diversas falencias, dificultades y dudas que surgen en
el ámbito financiero en la aplicación de métodos sencillos y eficaces a la hora
de conocer y aplicar conceptos básicos pero fundamentales de las ciencias o el
conocimiento financiero e incluso contable.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Entonces
surge la necesidad de generar un programa o aplicación que permita de una
manera didáctica y mediante el uso de herramientas tecnológicas, explicar
aquellos conceptos básicos y fundamentales sobre los que se cimentan algunos
conocimientos<span style="mso-spacerun: yes;"> </span>de las ciencias
financieras; permitiendo que el estudiante o micro empresario tenga una
aplicación en la cual pueda:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">1. Conocer y aplicar los
conceptos y fundamentos básicos financieros<span style="mso-spacerun: yes;">
</span>de aplicación o uso rutinario.</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">2. Servir de módulo de
pruebas</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">3. Servir de material de
consulta y referencia constante</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
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<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">4. Servir de apoyo al
docente como una<span style="mso-spacerun: yes;"> </span>herramienta tecnológica
la hora de guiar un tema específico en el software</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">INTRODUCCION</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">1.1 FINANMICRO (Sobre la Aplicación)</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Bienvenido
a la aplicación Finanmicro; esta guía le presenta conceptos básicos y
fundamentales sobre las funciones programadas en el software, al igual que
teoría básica con algunos ejemplos del material contenido en la aplicación.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
aplicación consta de 5 opciones o módulos integrados que permiten realizar
mediante<span style="mso-spacerun: yes;"> </span>procedimientos lógicos y
explicados por el mismo software, y claro está con la asesoría inicial del
docente;<span style="mso-spacerun: yes;"> </span>cálculos de interés simple, cálculos
de interés compuesto, conversión de tasas de interés,<span style="mso-spacerun: yes;"> </span>fondos de amortización<span style="mso-spacerun: yes;"> </span>y análisis financiero.</span></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es
una aplicación con un entorno práctico e intuitivo, pensado en estudiantes y
microempresarios con pocos o ningún conocimiento financiero o contable que a partir
de ejemplos y presentaciones permite su uso optimo y eficaz. </span></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">1.2 REQUERIMIENTOS E
INSTALACION</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
aplicación requiere que su computadora cuente con una de las siguientes
alternativas del sistema operativo: Windows Xp Sp3, Windows Vista, Windows 7 o
Windows 8; cualquiera de estas versiones debe tener instalado NetFramework 4.0
o superior (este último requerimiento si no lo cumple su sistema operativo,
puede descargarlo desde la internet desde el sitio de Microsoft </span><a href="http://www.microsoft.com/"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">www.microsoft.com</span></a><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">)</span></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Los
requerimientos de Hardware del equipo en el cual se va a ejecutar la aplicación
son mínimos, básicamente con que su computadora pueda ejecutar Windows Xp sp3.</span></div>
<br />
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">LAS MATEMATICAS FINANCIERAS Y ANALISIS FINANCIERO</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Antes
de entrar en detalle sobre como operar el software con cada uno de los módulos
y funciones, es necesario si así se requiere, hacer un repaso o introducirse
brevemente en el mundo de las matemáticas financieras, con el fin de hace un
uso correcto del software y evitar resultados inesperados o erróneos. </span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Las Matemáticas
Financieras:</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Las
matemáticas financieras constituyen un conjunto de herramientas propias de las
finanzas, necesarias en la operación y en las decisiones de los negocios. En
consecuencia deben ser conocidas por quienes tienen a cargo<span style="mso-spacerun: yes;"> </span>la elaboración, evaluación y dirección de los
planes financieros, si desean acertar en su gestión.</span></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Las
matemáticas financieras son una especie de subgrupo de las matemáticas puras,
con aplicación en lo que corresponde al dinero y a los negocios; una de las
premisas básicas del entorno financiero es que el tiempo es dinero; por ello
siempre se formularan casos en función del tiempo o es decir teniendo como
variable fundamental el tiempo en cada ejercicio financiero.</span></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
correcta aplicación de los conceptos básicos permitirá a la persona interesada
reconocer el valor del dinero a través del tiempo, así como reconocer y
realizar una planeación financiera adecuada para su entorno personal o su
empresa.</span></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> </span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Definiciones:</span></b>
</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Interés</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">: Es
el precio que se paga por el dinero que se toma en préstamo durante un periodo
de tiempo determinado. Puede definirse también como la utilidad o ganancia que
genera un capital o como el rendimiento de una inversión.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Valor Presente:</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> Es
la cantidad inicial de dinero que se toma o se entrega en préstamo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Valor Futuro:</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> Es
el valor más el interés </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Periodo:</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> Es
el intervalo de tiempo durante el valor presente gana interés, los periodos
pueden ser diversos (diario, semanal, mensual, bimensual, trimestral,
semestral, anual)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Tasa de interés:</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> Es
la relación entre el interés y valor presente generalmente se expresa en
porcentajes; es muy importante no confundir interés con tasa de interés, el
interés se representa en ganancia obtenida, mientras que la tasa de interés es
la representación porcentual.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo:
una tasa del 10% efectivo anual, una tasa del 2% capitalizable mensual.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> </span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><br /></span><br />
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div align="center" class="MsoListParagraph" style="line-height: 150%; margin-left: 54.0pt; mso-add-space: auto; mso-list: l14 level2 lfo5; text-align: center; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">2.1<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">INTERES SIMPLE</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Se
dice que una operación financiera se maneja bajo el concepto de interés simple,
cuando los intereses liquidados no se suman periódicamente al capital: es
decir, los intereses no devengan intereses. Sus características son las
siguientes:</span></div>
<div class="MsoListParagraphCxSpFirst" style="line-height: 150%; mso-list: l17 level1 lfo7; text-indent: -18.0pt;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El capital inicial no varía durante todo el
tiempo de la operación financiera, ya que los intereses no se suman al capital
inicial.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l17 level1 lfo7; text-indent: -18.0pt;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Como consecuencia de la característica
anterior, la tasa de interés siempre se aplicará sobre el mismo capital, es
decir, sobre el capital inicial.</span></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 150%; mso-list: l17 level1 lfo7; text-indent: -18.0pt;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Por la misma razón puede decirse que los
intereses serán siempre iguales en cada periodo. (*3)</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">La fórmula aplicada para solucionar muchos de
los casos es la siguiente:</span></div>
<div class="MsoNormal" style="margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 12.0pt;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 12.0pt;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">VF
= VP( 1 + T * i)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 5.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 12.0pt;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cada una de estas variables
se despeja por método algebraico, según se requiera.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Donde:</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">VP: Valor presente de la inversión</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">I: interés o dinero recibido en la inversión</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">i: Tasa de interés</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">VF: Valor Futuro de la inversión</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">T: Periodo de tiempo (en una fórmula más
adelante)</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo1:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cuál
será el valor a cancelar dentro de 10 meses por un préstamo de $ 5000000
recibidos en el día de hoy , si la tasa de interés simple es del 3.5% mensual?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP =
5´000.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i =
3.5 % mensual</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T=
10 meses</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I =
?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I = VP
X i<span style="mso-spacerun: yes;"> </span>= $ 5´000.000 X 3.5% = $ 175.000
para un mes</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Para
10 meses sería: $ 175.000 * 10 meses = $ 1´750.000 </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
VP + I = $ 5´000.000 + $ 1´750.000 = $ 6´750.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">En
solo intereses se estaría cancelando $ 1´750.000 + el capital adeudado $
5000000 = $ 6´750.000 este valor sería el valor futuro</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF=
$ 6´750.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> </span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo2:</span></b>
</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal; line-height: 150%;">Calcular a cuánto asciende el
interés simple producido por un capital de 25.000 pesos invertido durante 4
años a una tasa del 6 % anual.</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP =
25000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i =
6 % Anual</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T =
4 Años</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I =
?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I =
VP X i<span style="mso-spacerun: yes;"> </span>= $ 25.000 X 6% = $ 1500 para un
año</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Para
4 años sería: $ 15.000 X 4 años = $ 6000 </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
VP + I = $ 25.000 + $ 6000 = $ 31.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
$ 31.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> </span><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 3:</span></b>
</div>
<div style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "arial" , "sans-serif"; font-weight: normal;">Un préstamo
de $ 20.000 pesos se convierte al cabo de un año en $ 22.400 pesos. ¿Cuál es la
tasa de interés cobrada?</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span>I</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">i =<span style="mso-spacerun: yes;">
</span>--------- x 100</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-spacerun: yes;">
</span></span><span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">VP</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm; text-indent: 35.4pt;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">2400</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">i =<span style="mso-spacerun: yes;"> </span>--------------- x 100</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-spacerun: yes;"> </span>20.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = 12% </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo
4:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal; line-height: 150%;">Un capital de 300.000 pesos
invertido a una tasa de interés del 8% Mensual durante un cierto tiempo, ha
supuesto unos intereses de 48.000 pesos. ¿Cuánto tiempo ha estado invertido?</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP =
300.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
348.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i =
8 %</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T =
?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I = 48.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal;"><span style="mso-spacerun: yes;"> </span>1<span style="mso-spacerun: yes;"> </span>VF</span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal;">T
= ------- * ( ------------<span style="mso-spacerun: yes;"> </span>- 1) </span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal;"><span style="mso-spacerun: yes;"> </span>i<span style="mso-spacerun: yes;"> </span>VP</span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal;"><span style="mso-spacerun: yes;"> </span>1<span style="mso-spacerun: yes;"> </span>348.000</span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal;">T
= --------- * (---------------- -1) </span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal;"><span style="mso-spacerun: yes;"> </span>0.08<span style="mso-spacerun: yes;"> </span>300.000</span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal;">T
= 2 periodos o meses </span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal; line-height: 150%;"> </span></b><b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal; line-height: 150%;"></span></b><b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal; line-height: 150%;"> </span></b>
</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div align="center" class="MsoListParagraph" style="line-height: 150%; margin-left: 54.0pt; mso-add-space: auto; mso-list: l14 level2 lfo5; text-align: center; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">2.2<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">.INTERES COMPUESTO</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">A
diferencia del interés simple, aquí se suman periódicamente los intereses más
el capital. Este proceso de sumar los intereses al capital cada vez que se
liquiden se llama capitalización, y el periodo utilizado para liquidar los
intereses se llama periodo de capitalización.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">La formula general para resolver este tipo de
problemas es la siguiente:</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">VF = VP(1 + i)^T</span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Donde:</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">VF = Valor futuro</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">VP = Valor presente</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">(1+i)^T = Factor de capitalización en pago
único</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">i = Tasa de interés</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">T = Tiempo o periodos</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"> </span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"> </span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 1</span></b>
</div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Si se realiza una operación financiera
con una tasa de interés del 4% mensual, ¿Cuándo tiempo o meses se deben esperar
para que $500.000 de hoy se conviertan en $711.656.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
$ 711656</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP =
$ 500000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i =
4% Mensual</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T =
?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF = VP( 1+ i)^T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">711656 = 500000(1 + 0.04)^T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">(711656 / 500000) = (1 + 0.04)^T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">1.4233 = (1 + 0.04)^T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ahora aplicamos logaritmos, ya que la
ecuación presenta componente(s) exponenciales, entonces:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span></span><span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Log 1.4233 = T Log 1.04</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T =
(Log 14233 / Log 1.04)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T = (0.1533 / 0.0170) = 9</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T = 9 Periodos o meses<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 36.0pt; margin-right: 0cm; margin-top: 0cm; mso-add-space: auto;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 2</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Se depositan $ 1000000 durante un año,
en una corporación que reconoce el 3% mensual. Calcular el valor acumulado al
final del año.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF = VP( 1+ i)^T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP =
$1000000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i =
3%</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T =
12</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
1000000(1 + 0.03 )^12</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
1000000 * 1,425760886</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF = $ 1425760,88</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 3</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El señor Perez entra a trabajar a una
empresa ganando un sueldo mensual de $ 200.000 y espera recibir un aumento
anual promedio del 20%. ¿Cuánto quedará ganando después de 5 años?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = 200000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = 20%</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T = 5</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
VP( 1+ i)^T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
200000(1+0.020)^5</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF = $497.664</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 4</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Un inversionista acepto, inicialmente,
recibir $ 50.000.000 después de dos años, por la venta de una propiedad. Recibe
dos ofertas: Pedro y juan le ofrecen<span style="mso-spacerun: yes;"> </span>pagarle
hoy un valor equivalente, calculado así: Pedro, con una tasa de 2% mensual y
juan con una tasa del 3% mensual. ¿Que oferta debe aceptar?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF = VP( 1+ i)^T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Despejando VP:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = ( VF / (1 + i )^T)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Oferta
de Pedro:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = (50.000.000/(1 + 0.02)^24)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = $ 31.086.074,40</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Oferta
de Juan:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = (50.000.000 /(1 + 0.03)^24)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = $ 24´596.686,82</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 5</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Si en el día de hoy se invierten $ 100 y
después de año y medio se tienen acumulados $ 200 ¿ que tasa de interés arrojó
la operación?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = 100</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = ?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T = 18</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF = 200</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF = VP( 1+ i )^T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Aplicando Logaritmos:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">LogVF
= LogVP + TLog( 1 + i )</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">LogVF
– LogVP = TLog( 1 + i )</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Log(
1 + i ) = ((LogVF – LogVP) / T)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Log(
1 + i ) = ((Log200 – Log100) / 18)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Log(
1 + i ) = 0,0167</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">( 1 + i ) = Antilogaritmo 0,0167</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">( 1 + i ) = 1,0393</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = 0,0393 = 3,93 % mensual</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div align="center" class="MsoListParagraph" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l14 level2 lfo5; text-align: center; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.3<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">TASAS DE INTERES</span></b></div>
<div align="left" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm; text-align: left;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Interés:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es el precio que se paga por el uso del dinero que
se toma en préstamo durante un periodo de tiempo determinado. Puede definirse
también como utilidad o ganancia que genera un capital o como el rendimiento de
una inversión.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Interés
simple:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Se denomina interés simple al interés que se aplica
siempre sobre el capital inicial, debido a que los intereses generados no se
capitalizan.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El interés simple es un tipo de interés que siempre
se calcula sobre el capital inicial sin la capitalización de los intereses, de
suerte que los intereses generados no se incluyen en el cálculo futuro de los
intereses, permaneciendo el capital fijo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Interés
compuesto</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es la integración periódica del interés al capital.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Tasa de
Interés:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es la relación entre el interés y el valor presente.
Generalmente se expresa en porcentaje.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Tasa
nominal</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es la tasa que se declara en las operaciones
financieras y que es aparente por cuanto no refleja toda la realidad.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Tasa
efectiva</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es la tasa que se utiliza para determinar el interés
periódico que efectivamente debe sumarse al capital en el momento de la
liquidación. La tasa efectiva puede darse diaria, semanal, mensual, anual,
bianual etc.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
relación que existe entre la tasa nominal y la tasa efectiva, es la misma que
existe entre el interés simple y en interés compuesto; lo anterior significa
que la tasa nominal trabaja como interés simple y la tasa efectiva como interés
compuesto.</span><b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Periodo
de capitalización:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es la fracción de tiempo para la cual se liquida la
tasa de interés.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Tasas Equivalentes:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Dos
tasas de interés son equivalentes cuando ambas, obrando en condiciones
diferentes producen la misma tasa efectiva anual o el mismo valor futuro. El
concepto de “operar en condiciones diferentes” hace referencia a que ambas
capitalizan en periodos diferentes, o que una de ellas es vencida y la otra
anticipada. Esto indica, por ejemplo, que para una tasa mensual existe una
mensual anticipada equivalente, una tasa trimestral vencida equivalente, una
tasa trimestral anticipada equivalente, etc. Esta equivalencia de tasas también
se presenta entre tasas efectivas y nominales, o entre tasas nominales, es
decir, para una tasa mes vencido, existirá una tasa trimestre vencido
equivalente, una tasa trimestre anticipado equivalente etc.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Si
sobre una inversión se aplica una tasa mensual durante 12 meses y nos produce
el mismo resultado que aplicar sobre la misma inversión una tasa anual durante
un año, estas dos tasas (la mensual y la anual) son tasas equivalentes. Esta
operación también es conocida como equivalencia de intereses.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Para
aplicar mejor expresado, se resolverán algunos ejemplos, los cuales están
también plenamente detallados en la sección del software que corresponde a la
conversión de tasas; los ejemplos aquí resueltos por medio de ecuaciones y la
ayuda del software, le permitirá de una manera didáctica aprender estos
conceptos y hacer infinitas pruebas del tema con el software.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Conversión de tasas
de interés:</span></b></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Para
hallar la equivalencia entre tasas por lo general se usa la siguiente
formulación:</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Nominales
vencidas = <span style="mso-tab-count: 1;"> </span>(1 + ( J / F ))^F</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Nominales
anticipadas = <span style="mso-tab-count: 1;"> </span>(1 / (1 – (JD/F)))^F</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Periódicas
vencidas = <span style="mso-tab-count: 1;"> </span>(1 + iP )^F</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Periódicas
anticipadas =<span style="mso-tab-count: 1;"> </span>(1 / (1- D))^F</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Efectivas
=<span style="mso-tab-count: 3;"> </span>(1 + i )<span style="mso-tab-count: 2;"> </span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">J
= Tasa nominal vencida</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">F
= Frecuencia de Conversión</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">JD
= Tasa Nominal anticipada</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">iP
= Tasa de interés periódica vencida</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">D
= Tasa periódica anticipada</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">i
= Tasa efectiva</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraph" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l8 level1 lfo8; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Hallar
la tasa mensual vencida o equivalente al 6% trimestral vencida</span></b></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Solución:</span></b></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 + iP )^F =
(1 + iP )^F</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 + 0,06 )^4
= (1 + Ip )^12</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1,06)^(4/12)
= 1 + iP</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1,06)^(4/12)
– 1 = iP = 0,019612822</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">1,9612822 %
Mensual</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l8 level1 lfo8; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Hallar
la tasa mensual anticipada equivalente al 6% trimestral vencido</span></b></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Solución:</span></b></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 + 0,06)^4
= (1 / (1- D))^12</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1,06)^(4/12)
= (1 / (1 – D))</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">[
(1,06)^(4/12) ] * (1 – D) = 1</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 /
(1,06)^(4/12))) = 1 – D</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">0,980764441 =
1 – D</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">0,98076 -1 =
- D</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">0,0192355 = -
D * (- 1)</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">= 0,0192355 =
D</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">1,92355 %
Mensual anticipada</span></div>
<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l8 level1 lfo8; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Hallar
la tasa equivalente al 30% mensual</span></b></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Solución:</span></b></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 + 0,30) =
(1 + iP )^12</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1
+0,30)^(1/12) = (1 + iP) </span></div>
<div class="MsoListParagraphCxSpFirst">
<span style="font-family: "arial" , "sans-serif";">(1
+ 0,30)^(1/12) -1 = iP = 0,221 = 2.21 % Mensual</span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l8 level1 lfo8; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Hallar
la tasa equivalente al 30% bimensual</span></b></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Solución:</span></b></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";"><span style="mso-spacerun: yes;"> </span>(1 + 0,30) = (1 + iP )^6</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1
+0,30)^(1/6) = (1 + iP) </span></div>
<div class="MsoListParagraphCxSpFirst">
<span style="font-family: "arial" , "sans-serif";">(1
+ 0,30)^(1/6) -1 = iP = 0,446975 = 4,469750 % Mensual</span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l8 level1 lfo8; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Convertir
una tasa del 24.50% trimestre anticipada en nominal</span></b></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Solución:</span></b></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 / (1 – (JD
/ F)))^F = (1 + (J / F))^F</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 / (1 –
(0,245 / 4)))^4 = (1 + (J / 12)^12</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 / (1 –
(0,245 / 4)))^(4/12) =(1 + (J/12))</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">[(1 / (1 –
(0,245 / 4)))^(4/12)-1] * 12 = J = 0.2555 Mes vencido</span></div>
<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l8 level1 lfo8; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">6.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Convertir
una tasa del 85% Efectiva a Nominal mes vencido</span></b></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Solución:</span></b></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 + 0,85) =
(1 + (J / F)^F</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(1 + 0,85) =
(1 + (J /12)^12</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">(+
+0,85)^(1/12) = (1 + (J / 12)</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">((1 +
0,85)^(1/12)) – 1 = (J / 12)</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">((1 + 0,85)^(1/12))
– 1)* 12 = J</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">J = 0,631227</span></div>
<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l8 level1 lfo8; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">7.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Convertir
una tasa del 8% trimestral en semestral</span></b></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Solución:</span></b></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">((1 +
0,08)^(4/2))- 1 = iP</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif";">iP = 0,1664</span></div>
<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l8 level1 lfo8; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">8.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Convertir
una tasa del 8% trimestral en mensual</span></b></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">((1 + iP)^(F/F´)- 1=iP</span></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">((1+0,08)^(4/12)) – 1 = iP</span></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">iP = 0,0259855 </span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">2.4 Fondos de Amortización</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La amortización es desde el punto de vista
financiero, el proceso de pago de una deuda y sus intereses mediante una serie
de cuotas (periódicas o no), en un tiempo determinado.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Por lo general, cada cuota de pago que amortiza una deuda
tiene dos componentes: interés y abono a capital.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Al diseñar un plan de amortización de una deuda se
acostumbra a construir la tabla de amortización, que registra periodo a
periodo, la forma de cómo va evolucionando el pago de la deuda. Una tabla de amortización
debe tener mínimo 5 columnas, la primera muestra los periodos de pago, la
segunda muestra el valor de los intereses, la tercera el valor de de la cuota
periódica, la cuarta el abono a capital y la quinta columna muestra el saldo de
la deuda.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Los sistemas de amortización más utilizados en el
sistema financiero y comercial son:</span></div>
<div class="MsoListParagraphCxSpFirst" style="line-height: 150%; mso-list: l10 level1 lfo9; text-indent: -18.0pt;">
<span style="font-family: "symbol"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Amortización con
pago único del capital a final del plazo</span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l10 level1 lfo9; text-indent: -18.0pt;">
<span style="font-family: "symbol"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Amortización
Gradual</span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l10 level1 lfo9; text-indent: -18.0pt;">
<span style="font-family: "symbol"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Amortización
Gradual con cuotas extraordinarias</span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l10 level1 lfo9; text-indent: -18.0pt;">
<span style="font-family: "symbol"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Amortización con
periodo de gracia</span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l10 level1 lfo9; text-indent: -18.0pt;">
<span style="font-family: "symbol"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Amortización con
abono constante a capital</span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l10 level1 lfo9; text-indent: -18.0pt;">
<span style="font-family: "symbol"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Amortización con
interés global</span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l10 level1 lfo9; text-indent: -18.0pt;">
<span style="font-family: "symbol"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Amortización con
cuotas crecientes en forma lineal</span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l10 level1 lfo9; text-indent: -18.0pt;">
<span style="font-family: "symbol"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Amortización con
cuotas crecientes en forma geométrica</span></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 150%; mso-list: l10 level1 lfo9; text-indent: -18.0pt;">
<span style="font-family: "symbol"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Amortización con
cuotas mensuales fijas, crecientes anualmente en un porcentaje fijo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Para el desarrollo de algunos de los ejemplos que
funcionan en la sección del software que corresponde a fondo de amortización,
se utilizara un sistema que es muy tradicional en nuestra región para el pago
amortizado de créditos comerciales a nivel general; dicho sistema es el de
amortización gradual.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Las fórmulas que se usa para resolver a algunos de
los ejercicios son las siguientes:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">A = R * (1 – (((1 + i)^ - n)
/ i))</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I = A * i * T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Donde:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">A = Valor presente de una deuda</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = Tasa de interés</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">n = Periodos o numero de pagos</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">R =Valor de las cuotas periódicas</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I = Intereses</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="line-height: 150%; margin-left: 0cm; mso-add-space: auto; mso-list: l15 level1 lfo16; text-indent: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Un terreno que
cuesta $ 20.000.000 se propone comprar con una cuota inicial del 10% y 36
cuotas mensuales con una tasa de interés del 2% mensual. Calcular el valor de
las cuotas.</span></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">R = A [( (i *(1 + i)^n) / ((1 + i)^n)-1)]</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Al restarle el valor del terreno la cuota inicial de
$ 2´000.000 queda el saldo de la deuda que se va a financiar por medio de 36
cuotas mensuales.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Valor a financiar = $ 20´000.000 – $ 2´000.000 = $ 18´000.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">R = 18´000.000 [((0,02 *(1,02)^36)/((1,02)^36) -1)]</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span>A = $
706.191,35</span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Tabla de Amortización</span></b></div>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-yfti-tbllook: 1184; width: 552px;">
<tbody>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; height: 19.85pt; mso-border-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="top" width="85"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Periodo</span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Intereses</span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="top" width="104"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cuota</span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Abono Capital</span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="top" width="117"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Saldo</span></b></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">1</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">360000</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">346191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">17653808,7</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">2</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">353076,173</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">353115,174</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">17300693,5</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 3;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">3</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">346013,87</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">360177,477</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">16940516</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 4;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">4</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">338810,32</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">367381,027</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">16573135</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 5;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">5</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">331462,7</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">374728,647</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">16198406,3</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 6;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">6</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">323968,127</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">382223,22</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">15816183,1</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 7;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">7</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">316323,662</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">389867,685</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">15426315,4</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 8;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">8</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">308526,308</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">397665,038</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">15028650,4</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 9;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">9</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">300573,008</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">405618,339</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">14623032</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 10;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">10</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">292460,641</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">413730,706</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">14209301,3</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 11;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">11</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">284186,027</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">422005,32</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">13787296</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 12;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">12</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">275745,92</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">430445,426</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">13356850,6</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 13;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">13</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">267137,012</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">439054,335</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">12917796,3</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 14;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">14</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">258355,925</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">447835,422</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">12469960,8</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 15;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">15</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">249399,217</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">456792,13</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">12013168,7</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 16;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">16</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">240263,374</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">465927,973</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">11547240,7</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 17;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">17</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">230944,815</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">475246,532</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">11071994,2</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 18;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">18</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">221439,884</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">484751,463</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">10587242,7</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 19;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">19</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">211744,855</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">494446,492</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">10092796,2</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 20;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">20</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">201855,925</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">504335,422</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">9588460,83</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 21;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">21</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">191769,217</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">514422,13</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">9074038,7</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 22;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">22</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">181480,774</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">524710,573</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">8549328,12</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 23;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">23</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">170986,562</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">535204,784</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">8014123,34</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 24;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">24</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">160282,467</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">545908,88</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">7468214,46</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 25;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">25</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">149364,289</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">556827,058</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">6911387,4</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 26;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">26</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">138227,748</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">567963,599</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">6343423,8</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 27;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">27</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">126868,476</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">579322,871</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">5764100,93</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 28;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">28</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">115282,019</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">590909,328</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">5173191,6</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 29;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">29</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">103463,832</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">602727,515</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">4570464,09</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 30;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">30</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">91409,2818</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">614782,065</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">3955682,02</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 31;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">31</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">79113,6405</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">627077,706</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">3328604,32</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 32;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">32</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">66572,0864</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">639619,26</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">2688985,06</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 33;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">33</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">53779,7012</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">652411,646</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">2036573,41</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 34;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">34</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">40731,4682</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">665459,879</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">1371113,53</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 35;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">35</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">27422,2707</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">678769,076</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">692344,458</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 36; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.95pt;" valign="bottom" width="85"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">36</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">13846,8892</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 78.0pt;" valign="bottom" width="104"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">706191,347</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="bottom" width="123"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">692344,458</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 87.6pt;" valign="bottom" width="117"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">3,76E-08</span></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoListParagraph" style="line-height: 150%; margin-left: 0cm; mso-add-space: auto; mso-list: l15 level1 lfo16; text-indent: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Un electrodoméstico
que vale de contado $ 5000.000 se financia de la siguiente forma: una cuota
inicial de $500.000, y el saldo en 6 cuotas mensuales iguales. Si la tasas de
interés de financiación que se cobra es del 2.5% mensual, calcular el valor de
las cuotas.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b><span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoListParagraphCxSpFirst">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">5000000 = 500.000 + A * [((1 + i)^n)-1) / (i *(1 + i)^n)]</span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">5000000 = 500.000 + A * [((1 +
0.025)^6) -1) / (0.025 * (1+ 0.025)^6)]</span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">A = $ 816.974,87</span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Tabla de Amortización</span></b></div>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-yfti-tbllook: 1184; width: 561px;">
<tbody>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; height: 19.85pt; mso-border-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 67.55pt;" valign="top" width="90"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Periodo</span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="top" width="113"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Intereses</span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 85.2pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cuota</span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 99.05pt;" valign="top" width="132"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Abono Capital</span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 84.15pt;" valign="top" width="112"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Saldo</span></b></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 67.55pt;" valign="bottom" width="90"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">1</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="bottom" width="113"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">112500</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 85.2pt;" valign="bottom" width="114"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">816974,87</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 99.05pt;" valign="bottom" width="132"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">704474,87</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 84.15pt;" valign="bottom" width="112"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">3795525,13</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 67.55pt;" valign="bottom" width="90"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">2</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="bottom" width="113"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">94888,1283</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 85.2pt;" valign="bottom" width="114"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">816974,87</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 99.05pt;" valign="bottom" width="132"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">722086,742</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 84.15pt;" valign="bottom" width="112"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">3073438,39</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 3;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 67.55pt;" valign="bottom" width="90"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">3</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="bottom" width="113"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">76835,9597</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 85.2pt;" valign="bottom" width="114"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">816974,87</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 99.05pt;" valign="bottom" width="132"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">740138,91</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 84.15pt;" valign="bottom" width="112"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">2333299,48</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 4;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 67.55pt;" valign="bottom" width="90"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">4</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="bottom" width="113"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">58332,487</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 85.2pt;" valign="bottom" width="114"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">816974,87</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 99.05pt;" valign="bottom" width="132"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">758642,383</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 84.15pt;" valign="bottom" width="112"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">1574657,1</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 5;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 67.55pt;" valign="bottom" width="90"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">5</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="bottom" width="113"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">39366,4274</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 85.2pt;" valign="bottom" width="114"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">816974,87</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 99.05pt;" valign="bottom" width="132"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">777608,442</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 84.15pt;" valign="bottom" width="112"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">797048,653</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 6; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 67.55pt;" valign="bottom" width="90"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">6</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="bottom" width="113"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">19926,2163</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 85.2pt;" valign="bottom" width="114"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">816974,87</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 99.05pt;" valign="bottom" width="132"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">797048,653</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 19.85pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-height-rule: exactly; padding: 0cm 3.5pt 0cm 3.5pt; width: 84.15pt;" valign="bottom" width="112"><div align="center" class="MsoNormal" style="margin-bottom: .0001pt; margin: 0cm; text-align: center;">
<span style="color: black; font-family: "arial" , "sans-serif"; font-size: 12.0pt;">-1,56E-08</span></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%;">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 150%; margin-left: 0cm; mso-add-space: auto; mso-list: l15 level1 lfo16; text-indent: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ramón desea tener
$12.000 para darlos de enganche para una casa. Si puede ahorrar $1.300 cada mes
en un banco que le paga una tasa de interés del 2.24% mensual ¿Cuánto tiempo
tardará en acumular los $12.000.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 18.0pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 18.0pt;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">12000
= 1300 * [((1 + 0.0224)^n)-1) / (0.0224))]</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">n
= 8.48 meses </span></div>
<div class="MsoListParagraphCxSpFirst" style="line-height: 150%;">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 150%; margin-left: 0cm; mso-add-space: auto; mso-list: l15 level1 lfo16; text-indent: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Una deuda de
5000000 será cancelada mediante 6 cuotas mensuales iguales de igual valor al
2,210445 mensual, hallar el valor de las cuotas</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">A = $ 5000000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = 2,210445%</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">n = 6</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">R = ?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">A = R * (1 – ((1 + i )^ -n) / i)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">5000000 = R * (1 – ((1 + 0,02210445)^-6) /
0,02210445)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">5000000 = R * (5,5616865)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">R = (5000000 / 5,561865)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">R = $ 898.978 Valor de la cuota</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I = A * i * T</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I = 5000000 * 0.02210445 *1</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I = $110.522</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Abono a capital = cuota – intereses</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Sueldo = Saldo anterior – abono a capital</span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Tabla de Amortización</span></b></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 75.1pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Periodo</span></b></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.45pt;" valign="top" width="121"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Intereses</span></b></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.2pt;" valign="top" width="120"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cuota</span></b></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.05pt;" valign="top" width="139"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Abono Capital</span></b></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 92.9pt;" valign="top" width="124"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Saldo</span></b></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 1;">
<td style="border-top: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 75.1pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">0</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.45pt;" valign="top" width="121"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">0</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.2pt;" valign="top" width="120"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">0</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.05pt;" valign="top" width="139"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">0</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 92.9pt;" valign="top" width="124"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">5000000</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 2;">
<td style="border-top: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 75.1pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">1</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.45pt;" valign="top" width="121"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">110522</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.2pt;" valign="top" width="120"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">898.978</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.05pt;" valign="top" width="139"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">788457</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 92.9pt;" valign="top" width="124"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">4211543,30</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 3;">
<td style="border-top: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 75.1pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">2</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.45pt;" valign="top" width="121"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">93094</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.2pt;" valign="top" width="120"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">898.978</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.05pt;" valign="top" width="139"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">805884</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 92.9pt;" valign="top" width="124"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">3405659</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 4;">
<td style="border-top: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 75.1pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">3</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.45pt;" valign="top" width="121"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">75280</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.2pt;" valign="top" width="120"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">898.978</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.05pt;" valign="top" width="139"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">823698</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 92.9pt;" valign="top" width="124"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">2581961</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 5;">
<td style="border-top: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 75.1pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">4</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.45pt;" valign="top" width="121"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">57073</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.2pt;" valign="top" width="120"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">898.978</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.05pt;" valign="top" width="139"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">841905</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 92.9pt;" valign="top" width="124"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">1740056</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 6;">
<td style="border-top: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 75.1pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">5</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.45pt;" valign="top" width="121"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">38463</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.2pt;" valign="top" width="120"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">898.978</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.05pt;" valign="top" width="139"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">860515</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 92.9pt;" valign="top" width="124"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">879541</span></div>
</td>
</tr>
<tr style="height: 19.85pt; mso-height-rule: exactly; mso-yfti-irow: 7; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid black 1.0pt; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 75.1pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">6</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.45pt;" valign="top" width="121"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">19442</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 90.2pt;" valign="top" width="120"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">898.978</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.05pt;" valign="top" width="139"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">879536</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 19.85pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-height-rule: exactly; padding: 0cm 5.4pt 0cm 5.4pt; width: 92.9pt;" valign="top" width="124"><div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">0</span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">2.5 ANÁLISIS
FINANCIERO</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El
análisis financiero es un método para establecer los resultados financieros de
las decisiones de negocios, aplicando las diferentes técnicas como análisis
horizontal, análisis vertical, los indicadores financieros y otros, con el fin
de diagnosticar la situación financiera de la misma y permitir presentar
conclusiones y recomendaciones<span style="mso-spacerun: yes;"> </span>para la
correcta toma de decisiones. </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Importancia</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
información obtenida mediante el análisis financiero es de gran importancia ya
que permite:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">A la
administración de la empresa: Evaluar la gestión, determinar la variación de
los resultados, de acuerdo con lo planeado y lo ejecutado, los controles
establecidos, sus puntos fuertes y puntos débiles en las finanzas.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">A
los propietarios: Conocer los niveles de rentabilidad de su inversión en la
empresa, el crecimiento de la misma y los resultados que sirven de base para la
toma de decisiones.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">A
los bancos y acreedores: Saber la liquidez y la capacidad de pago de la empresa
y las posibilidades de conceder préstamo al negocio en las actuales
circunstancias.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Técnicas</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Las
técnicas de análisis financiero son los procedimientos utilizados para
simplificar o reducir los datos descriptivos y numéricos que integran<span style="mso-spacerun: yes;"> </span>los estados financieros, con el objeto de
medir diferentes relaciones en un mismo periodo y los cambios presentados en
diferentes periodos contables, comparar resultados alcanzados con las metas
planeadas, los controles aplicados , la rentabilidad y la capacidad de
endeudamiento, entre otros.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Herramientas de análisis financiero:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Análisis vertical</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es
un análisis estático, estudia la situación financiera en un momento determinado
y no tiene en cuenta los cambios ocurridos a lo largo del tiempo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Para
realizar este análisis se toma un solo estado financiero y se relaciona con un
total determinado (cifra base, que representa el 100%) cada una de sus partes.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Análisis Horizontal </span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es
una herramienta de análisis financiero que consiste en comparar estados
financieros homogéneos correspondientes a dos o más periodos consecutivos; al realizar
esta comparación se pueden observar los cambios obtenidos en las cuentas de
activo pasivo y patrimonio, ingreso, costo y gasto de una empresa en términos
de dinero.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razones o indicadores financieros</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Contablemente,
una razón financiera es el resultado de establecer la comparación numérica
entre las cifras correspondientes a dos cuentas de un mismo estado financiero,
o de dos estados financieros diferentes, con el propósito de formarse una idea
del comportamiento de algún aspecto, sector o área especifica de la empresa.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Las
razones financieras utilizadas con mayor frecuencia se han agrupado de acuerdo
con su utilidad, así:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razones
de liquidez</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razones
de actividad o rotación</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razones
de endeudamiento o apalancamiento</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razones
de rentabilidad</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razones
de valor de mercado de la empresa</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El
análisis de cada una de estas razones permite concluir el estado de la
situación financiera de la empresa.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El
software utiliza las principales razones financieras o las de uso común a la
hora de analizar un estado financiero; tales como:</span></i></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razón
corriente</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Capital
de trabajo neto</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Endeudamiento
financiero</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Rotación
de activos totales</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razón
de deuda</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Impacto
de la carga Financiera</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Endeudamiento
a corto plazo</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Indicadores
de apalancamiento</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Margen
de utilidad bruta sobre ventas</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razón Corriente (índice 1)</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es
una razón de liquidez de utilización frecuente, la cual mide la disponibilidad
a corto plazo que tiene el negocio para cubrir sus obligaciones del pasivo
corriente; este índice muestra con cuantos pesos del activo corriente de la empresa
se está respaldando cada peso de deuda inferior a un año.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
razón corriente indica la capacidad que tiene la empresa para cumplir con sus
obligaciones financieras, deudas o pasivos a corto plazo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Para
calcular dicho índice es necesario contar con los datos que nos suministra el
estado financiero en las cuentas correspondientes a activo corriente y pasivo
corriente, así:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Activo corriente: </span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal; line-height: 150%;">Se entiende por activos
corrientes aquellos activos que son susceptibles de convertirse en dinero en
efectivo en un periodo inferior a un año. Ejemplo de estos activos además de
caja y bancos, se tienen las inversiones a corto plazo, la cartera y los
inventarios</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">.</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Pasivo Corriente:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Los
pasivos corrientes hacen referencia a los pasivos (deudas) que la empresa debe
pagar en un plazo igual o inferior a un año.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Los
pasivos de una empresa se clasifican en aquellos pasivos a largo plazo y los
pasivos a corto plazo, esto es aquellas deudas que son exigibles en un corto
plazo, que son los que se conocen como pasivos corrientes.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Procedimiento
Matemático:</span></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="margin-left: 70.8pt; text-indent: 35.4pt;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Activo corriente</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Razón corriente =<span style="mso-spacerun: yes;"> </span>----------------------</span></div>
<div class="MsoNormal" style="margin-left: 70.8pt; text-indent: 35.4pt;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Pasivo corriente</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 2;"> </span>8000000</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Razón corriente =<span style="mso-spacerun: yes;"> </span>-------------- = 8</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 2;"> </span>1000000</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Endeudamiento Financiero (índice 2)</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es
un indicador que permite conocer en qué grado y de qué forman participan los
acreedores en la financiación de la empresa; así mismo, la capacidad que tiene
la empresa para acceder a nuevos créditos.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Para
calcular dicho índice es necesario contar con los datos que nos suministra el
estado financiero en las cuentas correspondientes a obligaciones financieras y
ventas netas, así:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Obligaciones Financieras:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Representa
el valor de los prestamos que la empresa ha recibido de entidades financieras;
(El valor de los prestamos recibidos por las entidades financieras)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ventas Netas:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Son
las "ventas brutas" menos el importe de las devoluciones,
bonificaciones, rebajas y descuentos.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Procedimiento
Matemático:</span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 2;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>Obligaciones Financieras x 100</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Endeudamiento Financiero = -----------------------------------------</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 4;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>Ventas Netas</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;">
</span><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>15000000 x 100</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Endeudamiento Financiero =
---------------------- = 15</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 2;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>100000000</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Razón de Deuda (índice 3):</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es
un indicador de endeudamiento que permite conocer en qué grado y de que forman
participan los acreedores en la financiación de la empresa; así mismo la
capacidad que tiene la empresa para acceder a nuevos créditos.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Este
índice en particular permite conocer el porcentaje de participación<span style="mso-spacerun: yes;"> </span>de los acreedores con relación<span style="mso-spacerun: yes;"> </span>a la financiación de los activos de la
empresa.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Para
calcular dicho índice es necesario contar con los datos que nos suministra el
estado financiero en las cuentas correspondientes a pasivo total y activo total
así:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Activo Total:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Son
todos los derechos y bienes que tiene una empresa.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Pasivo Total:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Son
todas las deudas y obligaciones que tiene la empresa.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Procedimiento
Matemático:</span></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>Pasivo Total x 100</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Razón de Deuda = ---------------------------</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>Activo Total</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 2;"> </span>15000000 * 100</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Razón de Deuda = ----------------------- =
18,75</span></div>
<div class="MsoNormal">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 2;"> </span><span style="mso-spacerun: yes;"> </span>80000000</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Endeudamiento a corto plazo (índice 4):</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Es
un indicador de endeudamiento que indica qué porcentaje de los pasivos tienen
vencimientos a menos de un año.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Para
calcular dicho índice es necesario contar con los datos que nos suministra el
estado financiero en las cuentas correspondientes a pasivo corriente y<span style="mso-spacerun: yes;"> </span>total pasivo así:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Pasivo Corriente:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Los
pasivos corrientes hacen referencia a los pasivos que la empresa debe pagar en
un plazo igual o inferior a un año.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Pasivo Total: </span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Son
todas las deudas y obligaciones que tiene la empresa.</span></div>
<div class="MsoNormal">
<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Procedimiento
Matemático:</span></b></div>
<div class="MsoNormal">
<br /></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 3;"> </span><span style="mso-spacerun: yes;"> </span>Pasivo corriente x 100</span></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Endeudamiento a Corto Plazo =
-------------------------------</span></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 2;"> </span><span style="mso-spacerun: yes;"> </span>Pasivo Total</span></div>
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<br /></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Endeudamiento a Corto Plazo =
---------------------- = 20</span></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 1 Razón Corriente</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene un activo corriente de $ 55´000.000 y un pasivo corriente de $
22´000.000; calcular la razón corriente.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Solución:
La empresa dispone de $ 2,5 del activo corriente como respaldo para cubrir cada
peso del pasivo inferior a un año.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 2 Capital de Trabajo Neto</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene un activo corriente de $ 55´000.000 y un pasivo corriente de $
22´000.000; calcular el capital neto de trabajo</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa cuenta con un capital neto de trabajo de $ 33´000.000 el cual le
permite pagar sus gastos operativos anuales, una vez cubiertos los valores de
las obligaciones a corto plazo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 3 Razón de Deuda</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene un activo total de $ 47´000.000 y un pasivo total de $
22´000.000; calcular la razón de deuda.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Quiere
decir que sobre el 46.80 % de los activos de la empresa tienen derecho los
acreedores por ser financiados por ellos; La razón de deuda es relativamente
baja, lo cual le permite acceso al crédito.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 4 Indicador de apalancamiento</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene un pasivo total de $ 22´0000.000 y un patrimonio de $ 25´000.000;
calcular el indicador de apalancamiento.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El
resultado indica que la empresa tiene un indicador de apalancamiento del 88%.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 5 Margen de utilidad bruta sobre
ventas </span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene una utilidad bruta sobre ventas de $ 15´000.000 y una ventas
netas por $ 20’000.000; Calcular el margen de utilidad bruta sobre ventas.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El
resultado significa que las ventas de la empresa generaron un 75 % de la
utilidad bruta.</span></div>
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<br /></div>
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<br /></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<br />
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<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Tabla normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:auto;
mso-para-margin-right:0cm;
mso-para-margin-bottom:auto;
mso-para-margin-left:36.0pt;
text-align:justify;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-fareast-language:EN-US;}
</style>
<![endif]-->
</div>
<div align="center" class="MsoListParagraph" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-align: center; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">FINANMICRO (DESCRIPCION DEL ENTORNO)</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Todo
el entorno de la aplicación se ejecuta en las versiones de Windows, por lo
tanto su presentación es a partir de ventanas como cualquier otra aplicación o
programa que se ejecute bajo Windows.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El
entorno ha sido diseñado de una manera intuitiva y con material de ayuda, lo
cual permitirá al usuario manejarlo a provechar al máximo sus funciones.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Pantalla
de inicio o de presentación del software</span></i></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-6ZcYAM8lWP0/UbovTyf0HDI/AAAAAAAAACQ/67Q15_hDhBw/s1600/Presentacion1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="272" src="https://4.bp.blogspot.com/-6ZcYAM8lWP0/UbovTyf0HDI/AAAAAAAAACQ/67Q15_hDhBw/s1600/Presentacion1.jpg" width="400" /></a></div>
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Esta
pantalla de presentación está compuesta por un botón que permite iniciar la
ventana con las opciones o módulos del software, también en su parte inferior
se encuentran tres links los cuales permiten ponerse en contacto con el
diseñador del software bien sea a través de su sitio en Facebook o a través de
los dos blogger diseñados para los módulos de prueba en sus etapa inicial.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ventana
con los respectivos botones que corresponden a cada una de las funciones
Financieras del Software.</span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> </span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> </span>
</div>
<div class="MsoListParagraph" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.1<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">ENTORNO INTERES SIMPLE</span></b></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Este
formulario o ventana al igual que la de los otros módulos está compuesta por
varios cuadros de texto y botones. </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Botón de Ayuda</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">: En
esta opción podrá encontrar ejemplos con respecto a la operación de este módulo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cada
uno de los módulos tiene este botón de ayuda el cual podrá utilizar para ver
algunos ejemplos sobre la forma en que se desarrollan los ejercicios que
corresponde a cada función.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-PRlqz6kUpLY/UbovuL1cv2I/AAAAAAAAACY/Qeyx3Ul1kYk/s1600/simple+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="275" src="https://1.bp.blogspot.com/-PRlqz6kUpLY/UbovuL1cv2I/AAAAAAAAACY/Qeyx3Ul1kYk/s1600/simple+1.jpg" width="320" /></a></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoListParagraph" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.2<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">ENTORNO INTERES COMPUESTO</span></b></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Este
formulario o ventana al igual que la de los otros módulos está compuesta por
varios cuadros de texto y botones. </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Botón de Ayuda</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">: En
esta opción podrá encontrar ejemplos con respecto a la operación de este
módulo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cada
uno de los módulos tiene este botón de ayuda el cual podrá utilizar para ver
algunos ejemplos sobre la forma en que se desarrollan los ejercicios que
corresponde a cada función.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-3gXgYuZuhTc/Ubov70Rr47I/AAAAAAAAACg/Ivp51g7IaHM/s1600/compuesto1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="260" src="https://4.bp.blogspot.com/-3gXgYuZuhTc/Ubov70Rr47I/AAAAAAAAACg/Ivp51g7IaHM/s1600/compuesto1.jpg" width="320" /></a></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoListParagraph" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.3<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">ENTORNO TASAS DE INTERES</span></b></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Este
formulario o ventana está compuesta por varios cuadros de texto, botones y
botones de selección. </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Botón de Ayuda</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">: En
esta opción podrá encontrar ejemplos con respecto a la operación de este
módulo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cada
uno de los módulos tiene este botón de ayuda el cual podrá utilizar para ver
algunos ejemplos sobre la forma en que se desarrollan los ejercicios que
corresponde a cada función.</span></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-36XLBROPPzY/UbowIWOxcwI/AAAAAAAAACo/3RoJ6iW3wpQ/s1600/tasa1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-36XLBROPPzY/UbowIWOxcwI/AAAAAAAAACo/3RoJ6iW3wpQ/s1600/tasa1.jpg" width="331" /></a></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<br /></div>
<div class="MsoListParagraph" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.4<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-spacerun: yes;"> </span>ENTORNO FONDOS DE
AMORTIZACION</span></b></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Este
formulario o ventana está compuesta por varios cuadros de texto, botones y una
tabla para el análisis de datos. </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Botón de Ayuda</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">: En
esta opción podrá encontrar ejemplos con respecto a la operación de este
módulo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cada
uno de los módulos tiene este botón de ayuda el cual podrá utilizar para ver
algunos ejemplos sobre la forma en que se desarrollan los ejercicios que
corresponde a cada función.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><a href="http://2.bp.blogspot.com/-nn3DSImhjew/UbowaFApVzI/AAAAAAAAACw/K9ONI6TF_DQ/s1600/fondo1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="145" src="https://2.bp.blogspot.com/-nn3DSImhjew/UbowaFApVzI/AAAAAAAAACw/K9ONI6TF_DQ/s1600/fondo1.jpg" width="400" /></a></b></div>
<br />
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoListParagraph" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.5<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-spacerun: yes;"> </span>ENTORNO INDICES
FINANCIEROS</span></b></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Este
formulario o ventana está compuesta por varios cuadros de texto y botones.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Botón de Ayuda</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">: En
esta opción podrá encontrar ejemplos con respecto a la operación de este
módulo.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cada
uno de los módulos tiene este botón de ayuda el cual podrá utilizar para ver
algunos ejemplos sobre la forma en que se desarrollan los ejercicios que
corresponde a cada función.</span></div>
<br />
<br />
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-bSJHZs_ZsCk/UbownvdRwpI/AAAAAAAAAC4/86RvszyiT5M/s1600/razonpresentacion.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="386" src="https://1.bp.blogspot.com/-bSJHZs_ZsCk/UbownvdRwpI/AAAAAAAAAC4/86RvszyiT5M/s1600/razonpresentacion.jpg" width="400" /></a></div>
<br />
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<br />
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<!--[if gte mso 9]><xml>
<o:OfficeDocumentSettings>
<o:RelyOnVML/>
<o:AllowPNG/>
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mso-ascii-theme-font:minor-latin;
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mso-hansi-theme-font:minor-latin;
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<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l2 level1 lfo1; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">TRABAJANDO CON EL SOFTWARE A PARTIR DE EJEMPLOS</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cada
uno de los ejemplos aquí presentados están dentro de la ayuda del software, y
están plenamente detallados y explicados en su planteamiento y solución por
medios matemáticos en la presente guía.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l2 level2 lfo1; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.1<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">INTERES SIMPLE</span></b></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo1:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Cuál
será el valor a cancelar dentro de 10 meses por un préstamo de $ 5000000
recibidos en el día de hoy , si la tasa de interés simple es del 3.5% mensual?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = 5´000.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = 3.5 % mensual</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T= 10 meses</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I = ?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Usando el software</span></b></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-irYHTkuX4cU/UbozupBeYsI/AAAAAAAAADI/qfcYt2x3b6U/s1600/simple+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="343" src="https://3.bp.blogspot.com/-irYHTkuX4cU/UbozupBeYsI/AAAAAAAAADI/qfcYt2x3b6U/s1600/simple+1.jpg" width="400" /></a></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo2:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Calcular
a cuánto asciende el interés simple producido por un capital de 25.000 pesos
invertido durante 4 años a una tasa del 6 % anual.</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = 25000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = 6 % Anual</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T = 4 Años</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I = ?</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Usando el software</span></b></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><a href="http://4.bp.blogspot.com/-5XsR4DkzNmk/Ubo0XQofLkI/AAAAAAAAADQ/aKhmfMCoiMM/s1600/simple+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="343" src="https://4.bp.blogspot.com/-5XsR4DkzNmk/Ubo0XQofLkI/AAAAAAAAADQ/aKhmfMCoiMM/s1600/simple+2.jpg" width="400" /></a></b></div>
<br />
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 3:</span></b></div>
<div style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "arial" , "sans-serif";">Un préstamo de $ 20.000 pesos se convierte al cabo de un
año en $ 22.400 pesos. ¿Cuál es la tasa de interés cobrada?</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";"></span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span>I</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">i =<span style="mso-spacerun: yes;">
</span>--------- x 100</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-spacerun: yes;">
</span>VP</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Usando el software</span></b></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-deoSrDh6LXo/Ubo0w4MaIZI/AAAAAAAAADY/zaQ0gWWz5Yc/s1600/simple+3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="343" src="https://3.bp.blogspot.com/-deoSrDh6LXo/Ubo0w4MaIZI/AAAAAAAAADY/zaQ0gWWz5Yc/s1600/simple+3.jpg" width="400" /></a></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 4:</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Un
capital de 300.000 pesos invertido a una tasa de interés del 8% Mensual durante
un cierto tiempo, ha supuesto unos intereses de 48.000 pesos. ¿Cuánto tiempo ha
estado invertido?</span></b><b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; font-weight: normal; line-height: 150%;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP =
300.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
348.000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i =
8 %</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T =
?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">I =
48.000</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Usando el software</span></b></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></b></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><a href="http://2.bp.blogspot.com/-VkcU2VHMCFU/Ubo0-vXPdNI/AAAAAAAAADg/BPMoFcnKUYM/s1600/simple+4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="342" src="https://2.bp.blogspot.com/-VkcU2VHMCFU/Ubo0-vXPdNI/AAAAAAAAADg/BPMoFcnKUYM/s1600/simple+4.jpg" width="400" /></a></b></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; margin-left: 54.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoListParagraph" style="line-height: 150%; margin-left: 54.0pt; mso-add-space: auto; mso-list: l2 level2 lfo1; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">2.2<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">INTERES COMPUESTO</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 1</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Si se realiza una operación financiera
con una tasa de interés del 4% mensual, ¿Cuándo tiempo o meses se deben esperar
para que $500.000 de hoy se conviertan en $711.656.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF =
$ 711656</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP =
$ 500000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i =
4% Mensual</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span lang="EN-US" style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T =
?</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Utilizando el
software</span></b></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><a href="http://2.bp.blogspot.com/-qO4dDlaQYdk/Ubo1WBLXeuI/AAAAAAAAADo/0AQ28vwGpFk/s1600/compuesto1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="325" src="https://2.bp.blogspot.com/-qO4dDlaQYdk/Ubo1WBLXeuI/AAAAAAAAADo/0AQ28vwGpFk/s1600/compuesto1.jpg" width="400" /></a></b></div>
<br />
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 2</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Se depositan $ 1000000 durante un año,
en una corporación que reconoce el 3% mensual. Calcular el valor acumulado al final
del año.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Utilizando el
software</span></b></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"></b></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><a href="http://4.bp.blogspot.com/-XPaKYV7YKPA/Ubo1gK6m_GI/AAAAAAAAADw/XyUuCg94IpA/s1600/compuesto2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-XPaKYV7YKPA/Ubo1gK6m_GI/AAAAAAAAADw/XyUuCg94IpA/s1600/compuesto2.jpg" /></a></b></div>
<br />
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 3</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">El
señor Perez entra a trabajar a una empresa ganando un sueldo mensual de $
200.000 y espera recibir un aumento anual promedio del 20%. ¿Cuánto quedará
ganando después de 5 años?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = 200000</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = 20%</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T = 5</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF = ?</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Utilizando el
software</span></b></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><a href="http://3.bp.blogspot.com/-hwKo5zYy9vM/Ubo13wncJ6I/AAAAAAAAAD4/9mrlQhfI51M/s1600/compuesto3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="323" src="https://3.bp.blogspot.com/-hwKo5zYy9vM/Ubo13wncJ6I/AAAAAAAAAD4/9mrlQhfI51M/s1600/compuesto3.jpg" width="400" /></a></b></div>
<br />
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 4</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Un inversionista acepto, inicialmente,
recibir $ 50.000.000 después de dos años, por la venta de una propiedad. Recibe
dos ofertas: Pedro y juan le ofrecen<span style="mso-spacerun: yes;">
</span>pagarle hoy un valor equivalente, calculado así: Pedro, con una tasa de
2% mensual y juan con una tasa del 3% mensual. ¿Que oferta debe aceptar?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<br /></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Utilizando el
software</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Oferta
de Pedro:</span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-pNka5iJOSaU/Ubo2K6EkVLI/AAAAAAAAAEA/6nroCvQs-9s/s1600/compuesto4a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="325" src="https://4.bp.blogspot.com/-pNka5iJOSaU/Ubo2K6EkVLI/AAAAAAAAAEA/6nroCvQs-9s/s1600/compuesto4a.jpg" width="400" /></a></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<br /></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Oferta
de Juan:</span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-tvH2Jf__JCo/Ubo2dZV5bAI/AAAAAAAAAEI/Y8wb1lXv4Yg/s1600/compuesto4b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="330" src="https://3.bp.blogspot.com/-tvH2Jf__JCo/Ubo2dZV5bAI/AAAAAAAAAEI/Y8wb1lXv4Yg/s1600/compuesto4b.jpg" width="400" /></a></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<br /></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">EJEMPLO 5</span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Si en el día de hoy se invierten $ 100 y
después de año y medio se tienen acumulados $ 200 ¿ que tasa de interés arrojó
la operación?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VP = 100</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">i = ?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">T = 18</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">VF = 200</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">Utilizando el
software</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
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<a href="http://1.bp.blogspot.com/-qGn0l7-PFzA/Ubo2snGQx3I/AAAAAAAAAEQ/ppjfK1EmqsQ/s1600/compuesto5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="326" src="https://1.bp.blogspot.com/-qGn0l7-PFzA/Ubo2snGQx3I/AAAAAAAAAEQ/ppjfK1EmqsQ/s1600/compuesto5.jpg" width="400" /></a></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.3<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">TASAS DE INTERES</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Hallar
la tasa mensual vencida o equivalente al 6% trimestral vencida</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Haciendo uso del Software</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-language: ES-CO; mso-no-proof: yes;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";"></span></b></div>
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<a href="http://1.bp.blogspot.com/-7zBlN8cqOBM/Ubo26uUNeVI/AAAAAAAAAEY/09j1Si0jtBE/s1600/tasa1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-7zBlN8cqOBM/Ubo26uUNeVI/AAAAAAAAAEY/09j1Si0jtBE/s1600/tasa1.jpg" width="331" /></a></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Hallar
la tasa mensual anticipada equivalente al 6% trimestral vencido</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Haciendo uso del Software</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; mso-fareast-language: ES-CO; mso-no-proof: yes;">
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<a href="http://3.bp.blogspot.com/-KGUc5PtBhP8/Ubo3OoiSsRI/AAAAAAAAAEg/NcHp9GoVc0w/s1600/tasa2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://3.bp.blogspot.com/-KGUc5PtBhP8/Ubo3OoiSsRI/AAAAAAAAAEg/NcHp9GoVc0w/s1600/tasa2.jpg" width="332" /></a></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Hallar
la tasa equivalente al 30% mensual</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Haciendo uso del Software</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; mso-fareast-language: ES-CO; mso-no-proof: yes;">
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<a href="http://4.bp.blogspot.com/-QOJ8HL2mvqw/Ubo3hpm8IrI/AAAAAAAAAEo/AH8Tic71-FM/s1600/tasa3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://4.bp.blogspot.com/-QOJ8HL2mvqw/Ubo3hpm8IrI/AAAAAAAAAEo/AH8Tic71-FM/s1600/tasa3.jpg" width="331" /></a></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Hallar
la tasa equivalente al 30% bimensual</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Haciendo uso del Software</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; mso-fareast-language: ES-CO; mso-no-proof: yes;">
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<a href="http://2.bp.blogspot.com/-XzVOckSxJm4/Ubo3yMUwLbI/AAAAAAAAAEw/ziELt7MQTXM/s1600/tasa4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://2.bp.blogspot.com/-XzVOckSxJm4/Ubo3yMUwLbI/AAAAAAAAAEw/ziELt7MQTXM/s1600/tasa4.jpg" width="333" /></a></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Convertir
una tasa del 24.50% trimestre anticipada en nominal</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Haciendo uso del Software</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-language: ES-CO; mso-no-proof: yes;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";"></span></b></div>
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<a href="http://1.bp.blogspot.com/-WrZ20v7uUk0/Ubo4Cn0w0eI/AAAAAAAAAE4/I2YnErin2u0/s1600/tasa5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-WrZ20v7uUk0/Ubo4Cn0w0eI/AAAAAAAAAE4/I2YnErin2u0/s1600/tasa5.jpg" width="335" /></a></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">6.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Convertir
una tasa del 85% Efectiva a Nominal mes vencido</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Haciendo uso del Software</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; mso-fareast-language: ES-CO; mso-no-proof: yes;">
</span><span style="font-family: "arial" , "sans-serif";"></span></div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-iQBDaK_UUkw/Ubo4RE0iG3I/AAAAAAAAAFA/oH7nM-CQLBU/s1600/tasa6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-iQBDaK_UUkw/Ubo4RE0iG3I/AAAAAAAAAFA/oH7nM-CQLBU/s1600/tasa6.jpg" width="331" /></a></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">7.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Convertir
una tasa del 8% trimestral en semestral</span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Haciendo uso del Software</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; mso-fareast-language: ES-CO; mso-no-proof: yes;">
</span><span style="font-family: "arial" , "sans-serif";"></span></div>
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<a href="http://1.bp.blogspot.com/-HD90XtE6mIg/Ubo4grsXPkI/AAAAAAAAAFI/WBk6dnq2AKM/s1600/tasa7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-HD90XtE6mIg/Ubo4grsXPkI/AAAAAAAAAFI/WBk6dnq2AKM/s1600/tasa7.jpg" width="333" /></a></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">8.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Convertir
una tasa del 8% trimestral en mensual</span></b></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Haciendo uso del Software</span></b></div>
<div align="center" class="MsoNormal" style="margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"></span></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-BcajL_ji1xI/Ubo4t1MqbCI/AAAAAAAAAFQ/JAyeZo6brXw/s1600/tasa8.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-BcajL_ji1xI/Ubo4t1MqbCI/AAAAAAAAAFQ/JAyeZo6brXw/s1600/tasa8.jpg" width="332" /></a></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.4<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">FONDOS DE AMORTIZACION</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Un terreno que cuesta $ 20.000.000 se propone
comprar con una cuota inicial del 10% y 36 cuotas mensuales con una tasa de
interés del 2% mensual. Calcular el valor de las cuotas.</span></div>
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<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Utilizando
el Software</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-M-hGiJad2fw/Ubo47xS9avI/AAAAAAAAAFY/UZIrlu3opkM/s1600/fondo1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="145" src="https://2.bp.blogspot.com/-M-hGiJad2fw/Ubo47xS9avI/AAAAAAAAAFY/UZIrlu3opkM/s1600/fondo1.jpg" width="400" /></a></div>
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<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l0 level1 lfo3; text-indent: -18.0pt;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Un electrodoméstico que vale de contado $ 5000.000
se financia de la siguiente forma: una cuota inicial de $500.000, y el saldo en
6 cuotas mensuales iguales. Si la tasas de interés de financiación que se cobra
es del 2.5% mensual, calcular el valor de las cuotas.</span></div>
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<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> </span></b><b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b><b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Utilizando
el Software</span></b></div>
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<a href="http://3.bp.blogspot.com/-UsHRyGoNYm8/Ubo5QFf4AwI/AAAAAAAAAFg/a7Yoex2Cr7Y/s1600/fondo2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="146" src="https://3.bp.blogspot.com/-UsHRyGoNYm8/Ubo5QFf4AwI/AAAAAAAAAFg/a7Yoex2Cr7Y/s1600/fondo2.jpg" width="400" /></a></div>
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<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"> </span></b>
</div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;">
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ramón desea tener
$12.000 para darlos de enganche para una casa. Si puede ahorrar $1.300 cada mes
en un banco que le paga una tasa de interés del 2.24% mensual ¿Cuánto tiempo
tardará en acumular los $12.000.</span></div>
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<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Utilizando
el Software</span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-lQRE1SlDPmA/Ubo5dkcjcYI/AAAAAAAAAFo/H2Yxkrymmj0/s1600/fondo3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="145" src="https://2.bp.blogspot.com/-lQRE1SlDPmA/Ubo5dkcjcYI/AAAAAAAAAFo/H2Yxkrymmj0/s1600/fondo3.jpg" width="400" /></a></div>
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<br /></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
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<br /></div>
<div class="MsoListParagraphCxSpLast" style="line-height: 150%; margin-left: 0cm; mso-add-space: auto; mso-list: l0 level1 lfo3; text-indent: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Una deuda de
5000000 será cancelada mediante 6 cuotas mensuales iguales de igual valor al
2,210445 mensual, hallar el valor de las cuotas</span></div>
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<b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Utilizando
el Software</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><a href="http://4.bp.blogspot.com/-1ZBzlLRKe_E/Ubo5s51pzRI/AAAAAAAAAFw/KAt--j4RbY0/s1600/fondo4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="143" src="https://4.bp.blogspot.com/-1ZBzlLRKe_E/Ubo5s51pzRI/AAAAAAAAAFw/KAt--j4RbY0/s1600/fondo4.jpg" width="400" /></a></b></div>
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<div class="MsoListParagraph" style="margin-left: 54.0pt; mso-add-space: auto; mso-list: l2 level2 lfo1; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-list: Ignore;">2.5<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt;"><span style="mso-spacerun: yes;"> </span>INDICES
FINANCIEROS</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 1 Razón Corriente</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene un activo corriente de $ 55´000.000 y un pasivo corriente de $
22´000.000; calcular la razón corriente.</span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Procedimiento con el Software:</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Calibri;"></span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><a href="http://2.bp.blogspot.com/-dmXUPtIIFbk/Ubo6GYPSOWI/AAAAAAAAAF4/Uey-r9HfUE0/s1600/razon1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="319" src="https://2.bp.blogspot.com/-dmXUPtIIFbk/Ubo6GYPSOWI/AAAAAAAAAF4/Uey-r9HfUE0/s1600/razon1.jpg" width="400" /></a></b></div>
<br />
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 2 Capital de Trabajo Neto</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene un activo corriente de $ 55´000.000 y un pasivo corriente de $
22´000.000; calcular el capital neto de trabajo.</span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Procedimiento con el Software:</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Calibri;"></span></b></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-INHxLEhttmo/Ubo6Tte50gI/AAAAAAAAAGA/CPH1v_B361E/s1600/razon2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="331" src="https://3.bp.blogspot.com/-INHxLEhttmo/Ubo6Tte50gI/AAAAAAAAAGA/CPH1v_B361E/s1600/razon2.jpg" width="400" /></a></div>
<br />
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 3 Razón de Deuda</span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene un activo total de $ 47´000.000 y un pasivo total de $ 22´000.000;
calcular la razón de deuda.</span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Procedimiento con el Software:</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Calibri;"></span></b></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-EH5D11TOLLI/Ubo6jDWR4SI/AAAAAAAAAGI/iDNG0ns4coY/s1600/razon3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="333" src="https://3.bp.blogspot.com/-EH5D11TOLLI/Ubo6jDWR4SI/AAAAAAAAAGI/iDNG0ns4coY/s1600/razon3.jpg" width="400" /></a></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
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<br /></div>
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<br /></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 4 Indicador de apalancamiento</span></b></div>
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<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene un pasivo total de $ 22´0000.000 y un patrimonio de $ 25´000.000;
calcular el indicador de apalancamiento.</span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Procedimiento con el Software:</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Calibri;"></span></b></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></b></div>
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<br /></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><a href="http://3.bp.blogspot.com/-VGNIDbx5WwY/Ubo6w5Vlw9I/AAAAAAAAAGQ/WI-Sx4lmC84/s1600/razon4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="321" src="https://3.bp.blogspot.com/-VGNIDbx5WwY/Ubo6w5Vlw9I/AAAAAAAAAGQ/WI-Sx4lmC84/s1600/razon4.jpg" width="400" /></a></b></div>
<br />
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<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">Ejemplo 5 Margen de utilidad bruta sobre
ventas </span></b><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">La
empresa tiene una utilidad bruta sobre ventas de $ 15´000.000 y una ventas
netas por $ 20’000.000; Calcular el margen de utilidad bruta sobre ventas.</span></div>
<div class="MsoNormal" style="margin-left: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif";">Procedimiento con el Software:</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "sans-serif"; mso-fareast-font-family: Calibri;"></span></b></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;">
</span><span style="font-family: "arial" , "sans-serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-nLaxAeCDmeY/Ubo7DrUw56I/AAAAAAAAAGY/Jqea_sZw7cs/s1600/razon5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="325" src="https://4.bp.blogspot.com/-nLaxAeCDmeY/Ubo7DrUw56I/AAAAAAAAAGY/Jqea_sZw7cs/s1600/razon5.jpg" width="400" /></a></div>
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<div class="MsoNormal" style="line-height: 150%; margin-left: 0cm; text-align: left;">
<span style="font-size: large;"><span style="color: red;">Si desea descargar la versión 2020 para dispositivos Android de este software lo puede hacer desde: <a href="https://play.google.com/store/apps/details?id=com.acme.financexpert" target="_blank">https://play.google.com/store/apps/details?id=com.acme.financexpert </a></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Más información sobre esta nueva versión en: </span></span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://finanexpert.blogspot.com/2020/01/software-para-el-diagnostico-analisis-y.html">https://finanexpert.blogspot.com/2020/01/software-para-el-diagnostico-analisis-y.html</a> </span></span><br />
<br />
<span style="font-size: large;"><span style="color: red;">Si desea adquirir el software para versión Pc puede escribirme al siguiente email: <a href="mailto:quindiofinanciero@hotmail.com">quindiofinanciero@hotmail.com</a> o agregarme a mi facebook:</span></span><br />
<span style="color: white;"><span style="font-size: large;"><a href="https://www.facebook.com/luisalberto.uriberomero">https://www.facebook.com/luisalberto.uriberomero</a></span></span><br />
<span style="color: red;"><span style="color: white;"><span style="font-size: large;"><a href="https://quindiofinanciero.wixsite.com/financiero" target="_blank">https://quindiofinanciero.wixsite.com/financiero </a></span></span></span><br />
<br />
<br />
<div style="text-align: justify;">
<span style="font-size: large;"><span style="color: red;"><span style="color: red;">También puede comunicarse a este número a través de whatsapp<span style="background-color: white;"><span style="color: lime;"><u><span class="post-content" style="display: block; font-size: medium; overflow: hidden; width: 710px;"><b><i><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></i></b></span><span class="post-content" style="display: block; font-size: medium; overflow: hidden; width: 710px;"><b><i><span style="font-family: "arial" , "helvetica" , sans-serif;"></span></i></b></span><span class="post-content" style="display: block; font-size: medium; overflow: hidden; width: 710px;"><b><i><span style="font-family: "arial" , "helvetica" , sans-serif;">WhatsApp: +57 3117341743</span></i></b></span></u></span></span></span></span></span><span style="font-size: large;"><span style="color: red;"><span style="color: red;"><span style="background-color: white;"><span style="color: lime;"><u><span style="color: blue;"><span class="post-content" style="display: block; font-size: medium; overflow: hidden; width: 710px;"><b><i><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></i></b></span></span></u></span></span></span></span></span><span style="font-size: large;"><span style="color: red;"><span style="color: red;"><span style="background-color: white;"><span style="color: lime;"><span class="post-content" style="display: block; font-size: medium; overflow: hidden; width: 710px;"><b><i><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></i></b></span><span style="color: red;"><span class="post-content" style="display: block; font-size: medium; overflow: hidden; width: 710px;"><b><i><span style="font-family: "arial" , "helvetica" , sans-serif;">El software se encuentra disponible para Computadoras con sistema operativo</span></i></b></span><span class="post-content" style="display: block; font-size: medium; overflow: hidden; width: 710px;"><b><i><span style="font-family: "arial" , "helvetica" , sans-serif;"> Windows y para SmartPhones o teléfonos con sistema operativo Android.</span></i></b></span><span class="post-content" style="display: block; font-size: medium; overflow: hidden; width: 710px;"><b><i><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></i></b></span></span></span></span></span></span></span><span style="color: white;"><span style="font-size: large;"><span style="color: red;"><span style="color: blue;"><u><span style="background-color: white;"><span class="post-content" style="display: block; font-size: medium; overflow: hidden; width: 710px;"><b><i><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></i></b></span></span></u></span></span></span></span></div>
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