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Matematicas Financieras: Tablas de tasas factores financieros (2020)

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SANTA CRUZ BOLIVIA
Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 2
PRESENTACION
En el proceso de calculó de operaciones financi...
Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 3
RELACIONES PARA FLUJOS DE EFECTIVO DISCRETOS CON
CAPITALIZAC...
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Matematicas Financieras: Tablas de tasas factores financieros (2020)

  1. 1. SANTA CRUZ BOLIVIA
  2. 2. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 2 PRESENTACION En el proceso de calculó de operaciones financieras a interés compuesto se presentan casos donde los reemplazos y calculo en las formulas o relaciones algebraicas requiere de agilidad y atención para no cometer errores redondeo y otros de tipo practico. Con el propósito de que en el proceso aprendizaje propio de la materia MAT250 y MAT300 se haga más versátil en cuanto se refiere al cálculo de Operaciones Financieras Académicas, es esta oportunidad presentamos un compendio de tablas financieras para el cálculo de: - Tasas de Interés equivalente. - Factores de cálculo Financiero. Sin embargo el objetivo final del curso es que el alumno debe saber realizar cálculos financieros aplicando medios digitales como ser las planillas de cálculo EXCEL. LA PRESENTACION CONTIENE:  FORMULARIOS: o Formulario de relaciones para el cálculo Algebraico o Formulario de relaciones para el cálculo Estándar  TASAS EQUIVALENTES: o Efectivas anuales (i), en función de tasas nominales periódicas (m) o Efectivas periódicas (i), en función de una tasa efectiva anual (i)  FACTORES DE CÁLCULO FINANCIERO: o Cantidad compuesta: F/P o Valor presente: P/F o Factor de amortización: A/F o Cantidad compuesta: F/A o Recuperación de capital: A/F o Valor presente: P/A o Gradiente de valor presente: P/G o Gradiente de serie anual: A/G ALUMNO: GRUPO: Elaborado Por: Ing. José Morón Rossel Docente Titular “C” Correo: jmoron@live.com Teléfono: 3704131 Pagina web: http://jmoronr.wordpress.com/ Aula Virtual: https://campus.chamilo.org SANTA CRUZ BOLIVIA
  3. 3. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 3 RELACIONES PARA FLUJOS DE EFECTIVO DISCRETOS CON CAPITALIZACION AL FINAL DEL PERIODO TIPO FACTOR FORMULA NOTACION ESTANDAR Cantidad única F/P (1 )n F P i  ( / , , )F P F P i n P/F 1 1 n P F i       ( / , , )P F P F i n Serie Uniforme P/A (1 ) 1 (1 ) n n i P A i i         ( / , , )P A P A i n A/P (1 ) (1 ) 1 n n i i A P i         ( / , , )A P A P i n F/A (1 ) 1n i F A i         ( / , , )F A F A i n A/F (1 ) 1n i A F i         ( / , , )A F A F i n Gradiente aritmético P/G 2 (1 ) 1 (1 ) n G n i in P G i i          ( / , , )GP G P G i n A/G 1 (1 ) 1 G n n A G i i         ( / , , )GA G A G i n Gradiente Geométrico P/D,E 0 (1 ) (1 ) ( )(1 ) n n n E i P D E i i          E i OTRAS FORMULAS IMPORTANTES TIPO FACTOR No D´ PERIODOS TASA Para Cantidad única F/P o P/F 1 ln( ) ln( ) ln( ) F p n i    1n F i p   Para serie uniforme P/A     ( ) ln ln ln(1 ) P Tiempo A A Pi n i     Función implícita F/A      ( ) ln ln ln 1 F Tiempo Fi A A n i     Función implícita
  4. 4. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 4
  5. 5. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 5 TASAS EQUIVALENTES
  6. 6. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 6 m Año Semestre Cuatrimestre trimestre bimestre mes dia continuo i 1 2 3 4 6 12 360 1000 1.0% 1.00% 0.50% 0.33% 0.25% 0.17% 0.083% 0.003% 0.001% 1.5% 1.50% 0.75% 0.50% 0.37% 0.25% 0.124% 0.004% 0.001% 2.0% 2.00% 1.00% 0.66% 0.50% 0.33% 0.165% 0.006% 0.002% 2.5% 2.50% 1.24% 0.83% 0.62% 0.41% 0.206% 0.007% 0.002% 3.0% 3.00% 1.49% 0.99% 0.74% 0.49% 0.247% 0.008% 0.003% 3.5% 3.50% 1.73% 1.15% 0.86% 0.58% 0.287% 0.010% 0.003% 4.0% 4.00% 1.98% 1.32% 0.99% 0.66% 0.327% 0.011% 0.004% 4.5% 4.50% 2.23% 1.48% 1.11% 0.74% 0.367% 0.012% 0.004% 5.0% 5.00% 2.47% 1.64% 1.23% 0.82% 0.407% 0.014% 0.005% 5.5% 5.50% 2.71% 1.80% 1.35% 0.90% 0.447% 0.015% 0.005% 6.0% 6.00% 2.96% 1.96% 1.47% 0.98% 0.487% 0.016% 0.006% 6.5% 6.50% 3.20% 2.12% 1.59% 1.06% 0.526% 0.017% 0.006% 7.0% 7.00% 3.44% 2.28% 1.71% 1.13% 0.565% 0.019% 0.007% 7.5% 7.50% 3.68% 2.44% 1.82% 1.21% 0.604% 0.020% 0.007% 8.0% 8.00% 3.92% 2.60% 1.94% 1.29% 0.643% 0.021% 0.008% 8.5% 8.50% 4.16% 2.76% 2.06% 1.37% 0.682% 0.023% 0.008% 9.0% 9.00% 4.40% 2.91% 2.18% 1.45% 0.721% 0.024% 0.009% 9.5% 9.50% 4.64% 3.07% 2.29% 1.52% 0.759% 0.025% 0.009% 10.0% 10.00% 4.88% 3.23% 2.41% 1.60% 0.797% 0.026% 0.010% 10.5% 10.50% 5.12% 3.38% 2.53% 1.68% 0.836% 0.028% 0.010% 11.0% 11.00% 5.36% 3.54% 2.64% 1.75% 0.873% 0.029% 0.010% 11.5% 11.50% 5.59% 3.70% 2.76% 1.83% 0.911% 0.030% 0.011% 12.0% 12.00% 5.83% 3.85% 2.87% 1.91% 0.949% 0.031% 0.011% 12.5% 12.50% 6.07% 4.00% 2.99% 1.98% 0.986% 0.033% 0.012% 13.0% 13.00% 6.30% 4.16% 3.10% 2.06% 1.02% 0.034% 0.012% 13.5% 13.50% 6.54% 4.31% 3.22% 2.13% 1.06% 0.035% 0.013% 14.0% 14.00% 6.77% 4.46% 3.33% 2.21% 1.10% 0.036% 0.013% 14.5% 14.50% 7.00% 4.62% 3.44% 2.28% 1.13% 0.038% 0.014% 15.0% 15.00% 7.24% 4.77% 3.56% 2.36% 1.171% 0.039% 0.014% 15.5% 15.50% 7.47% 4.92% 3.67% 2.43% 1.21% 0.040% 0.014% 16.0% 16.00% 7.70% 5.07% 3.78% 2.50% 1.24% 0.041% 0.015% 16.5% 16.50% 7.94% 5.22% 3.89% 2.58% 1.28% 0.042% 0.015% 17.0% 17.00% 8.17% 5.37% 4.00% 2.65% 1.32% 0.044% 0.016% 17.5% 17.50% 8.40% 5.52% 4.11% 2.72% 1.35% 0.045% 0.016% 18.0% 18.00% 8.63% 5.67% 4.22% 2.80% 1.39% 0.046% 0.017% 18.5% 18.50% 8.86% 5.82% 4.33% 2.87% 1.42% 0.047% 0.017% 19.0% 19.00% 9.09% 5.97% 4.44% 2.94% 1.46% 0.048% 0.017% 19.5% 19.50% 9.32% 6.12% 4.55% 3.01% 1.50% 0.049% 0.018% 20.0% 20.00% 9.54% 6.27% 4.66% 3.09% 1.531% 0.051% 0.018% 20.5% 20.50% 9.77% 6.41% 4.77% 3.16% 1.57% 0.052% 0.019% 21.0% 21.00% 10.00% 6.56% 4.88% 3.23% 1.60% 0.053% 0.019% 21.5% 21.50% 10.23% 6.71% 4.99% 3.30% 1.64% 0.054% 0.019% 22.0% 22.00% 10.45% 6.85% 5.10% 3.37% 1.67% 0.055% 0.020% 22.5% 22.50% 10.68% 7.00% 5.20% 3.44% 1.71% 0.056% 0.020% 23.0% 23.00% 10.91% 7.14% 5.31% 3.51% 1.74% 0.058% 0.021% 23.5% 23.50% 11.13% 7.29% 5.42% 3.58% 1.77% 0.059% 0.021% 24.0% 24.00% 11.36% 7.43% 5.53% 3.65% 1.81% 0.060% 0.022% 24.5% 24.50% 11.58% 7.58% 5.63% 3.72% 1.84% 0.061% 0.022% 25.0% 25.00% 11.80% 7.72% 5.74% 3.79% 1.88% 0.062% 0.022% TASA EFECTIVA PERIODICA i(m), EN FUNCION DE LA TASA EFECTIVA ANUAL i=(a)
  7. 7. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 7 m Año Semestre Cuatrimestre trimestre bimestre mes dia continuo i/m 1 2 3 4 6 12 360 1000 1.0% 1.00% 1.00% 1.00% 1.00% 1.00% 1.00% 1.01% 1.01% 1.5% 1.50% 1.51% 1.51% 1.51% 1.51% 1.51% 1.51% 1.51% 2.0% 2.00% 2.01% 2.01% 2.02% 2.02% 2.02% 2.02% 2.02% 2.5% 2.50% 2.52% 2.52% 2.52% 2.53% 2.53% 2.53% 2.53% 3.0% 3.00% 3.02% 3.03% 3.03% 3.04% 3.04% 3.05% 3.05% 3.5% 3.50% 3.53% 3.54% 3.55% 3.55% 3.56% 3.56% 3.56% 4.0% 4.00% 4.04% 4.05% 4.06% 4.07% 4.07% 4.08% 4.08% 4.5% 4.50% 4.55% 4.57% 4.58% 4.59% 4.59% 4.60% 4.60% 5.0% 5.00% 5.06% 5.08% 5.09% 5.11% 5.12% 5.13% 5.13% 5.5% 5.50% 5.58% 5.60% 5.61% 5.63% 5.64% 5.65% 5.65% 6.0% 6.00% 6.09% 6.12% 6.14% 6.15% 6.17% 6.18% 6.18% 6.5% 6.50% 6.61% 6.64% 6.66% 6.68% 6.70% 6.72% 6.72% 7.0% 7.00% 7.12% 7.16% 7.19% 7.21% 7.23% 7.25% 7.25% 7.5% 7.50% 7.64% 7.69% 7.71% 7.74% 7.76% 7.79% 7.79% 8.0% 8.00% 8.16% 8.22% 8.24% 8.27% 8.30% 8.33% 8.33% 8.5% 8.50% 8.68% 8.74% 8.77% 8.81% 8.84% 8.87% 8.87% 9.0% 9.00% 9.20% 9.27% 9.31% 9.34% 9.38% 9.42% 9.42% 9.5% 9.50% 9.73% 9.80% 9.84% 9.88% 9.92% 9.96% 9.97% 10.0% 10.00% 10.25% 10.34% 10.38% 10.43% 10.47% 10.52% 10.52% 10.5% 10.50% 10.78% 10.87% 10.92% 10.97% 11.02% 11.07% 11.07% 11.0% 11.00% 11.30% 11.41% 11.46% 11.52% 11.57% 11.63% 11.63% 11.5% 11.50% 11.83% 11.95% 12.01% 12.07% 12.13% 12.19% 12.19% 12.0% 12.00% 12.36% 12.49% 12.55% 12.62% 12.68% 12.75% 12.75% 12.5% 12.50% 12.89% 13.03% 13.10% 13.17% 13.24% 13.31% 13.31% 13.0% 13.00% 13.42% 13.57% 13.65% 13.72% 13.80% 13.88% 13.88% 13.5% 13.50% 13.96% 14.12% 14.20% 14.28% 14.37% 14.45% 14.45% 14.0% 14.00% 14.49% 14.66% 14.75% 14.84% 14.93% 15.02% 15.03% 14.5% 14.50% 15.03% 15.21% 15.31% 15.40% 15.50% 15.60% 15.60% 15.0% 15.00% 15.56% 15.76% 15.87% 15.97% 16.08% 16.18% 16.18% 15.5% 15.50% 16.10% 16.31% 16.42% 16.54% 16.65% 16.76% 16.76% 16.0% 16.00% 16.64% 16.87% 16.99% 17.11% 17.23% 17.35% 17.35% 16.5% 16.50% 17.18% 17.42% 17.55% 17.68% 17.81% 17.93% 17.94% 17.0% 17.00% 17.72% 17.98% 18.11% 18.25% 18.39% 18.53% 18.53% 17.5% 17.50% 18.27% 18.54% 18.68% 18.83% 18.97% 19.12% 19.12% 18.0% 18.00% 18.81% 19.10% 19.25% 19.41% 19.56% 19.72% 19.72% 18.5% 18.50% 19.36% 19.66% 19.82% 19.99% 20.15% 20.32% 20.32% 19.0% 19.00% 19.90% 20.23% 20.40% 20.57% 20.75% 20.92% 20.92% 19.5% 19.50% 20.45% 20.79% 20.97% 21.15% 21.34% 21.52% 21.53% 20.0% 20.00% 21.00% 21.36% 21.55% 21.74% 21.94% 22.13% 22.14% 20.5% 20.50% 21.55% 21.93% 22.13% 22.33% 22.54% 22.75% 22.75% 21.0% 21.00% 22.10% 22.50% 22.71% 22.93% 23.14% 23.36% 23.37% 21.5% 21.50% 22.66% 23.08% 23.30% 23.52% 23.75% 23.98% 23.98% 22.0% 22.00% 23.21% 23.65% 23.88% 24.12% 24.36% 24.60% 24.60% 22.5% 22.50% 23.77% 24.23% 24.47% 24.72% 24.97% 25.22% 25.23% 23.0% 23.00% 24.32% 24.81% 25.06% 25.32% 25.59% 25.85% 25.86% 23.5% 23.50% 24.88% 25.39% 25.65% 25.92% 26.20% 26.48% 26.49% 24.0% 24.00% 25.44% 25.97% 26.25% 26.53% 26.82% 27.11% 27.12% 24.5% 24.50% 26.00% 26.56% 26.84% 27.14% 27.45% 27.75% 27.76% TASA EFECTIVA ANUAL i(a), EN FUNCION DE LA TASA NOMINAL j(m)
  8. 8. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 8 m Año Semestre Cuatrimestre trimestre bimestre mes dia continuo i/m 1 2 3 4 6 12 360 1000 1.0% 1.00% 0.50% 0.33% 0.25% 0.17% 0.08% 0.003% 0.001% 1.5% 1.50% 0.75% 0.50% 0.38% 0.25% 0.13% 0.004% 0.002% 2.0% 2.00% 1.00% 0.67% 0.50% 0.33% 0.17% 0.006% 0.002% 2.5% 2.50% 1.25% 0.83% 0.63% 0.42% 0.21% 0.007% 0.003% 3.0% 3.00% 1.50% 1.00% 0.75% 0.50% 0.25% 0.008% 0.003% 3.5% 3.50% 1.75% 1.17% 0.88% 0.58% 0.29% 0.010% 0.004% 4.0% 4.00% 2.00% 1.33% 1.00% 0.67% 0.33% 0.011% 0.004% 4.5% 4.50% 2.25% 1.50% 1.13% 0.75% 0.38% 0.013% 0.005% 5.0% 5.00% 2.50% 1.67% 1.25% 0.83% 0.42% 0.01% 0.01% 5.5% 5.50% 2.75% 1.83% 1.38% 0.92% 0.46% 0.015% 0.006% 6.0% 6.00% 3.00% 2.00% 1.50% 1.00% 0.50% 0.017% 0.006% 6.5% 6.50% 3.25% 2.17% 1.63% 1.08% 0.54% 0.018% 0.007% 7.0% 7.00% 3.50% 2.33% 1.75% 1.17% 0.58% 0.019% 0.007% 7.5% 7.50% 3.75% 2.50% 1.88% 1.25% 0.63% 0.021% 0.008% 8.0% 8.00% 4.00% 2.67% 2.00% 1.33% 0.67% 0.022% 0.008% 8.5% 8.50% 4.25% 2.83% 2.13% 1.42% 0.71% 0.024% 0.009% 9.0% 9.00% 4.50% 3.00% 2.25% 1.50% 0.75% 0.025% 0.009% 9.5% 9.50% 4.75% 3.17% 2.38% 1.58% 0.79% 0.026% 0.010% 10.0% 10.00% 5.00% 3.33% 2.50% 1.67% 0.83% 0.03% 0.01% 10.5% 10.50% 5.25% 3.50% 2.63% 1.75% 0.88% 0.029% 0.011% 11.0% 11.00% 5.50% 3.67% 2.75% 1.83% 0.92% 0.031% 0.011% 11.5% 11.50% 5.75% 3.83% 2.88% 1.92% 0.96% 0.032% 0.012% 12.0% 12.00% 6.00% 4.00% 3.00% 2.00% 1.00% 0.033% 0.012% 12.5% 12.50% 6.25% 4.17% 3.13% 2.08% 1.04% 0.035% 0.013% 13.0% 13.00% 6.50% 4.33% 3.25% 2.17% 1.08% 0.036% 0.013% 13.5% 13.50% 6.75% 4.50% 3.38% 2.25% 1.13% 0.038% 0.014% 14.0% 14.00% 7.00% 4.67% 3.50% 2.33% 1.17% 0.039% 0.014% 14.5% 14.50% 7.25% 4.83% 3.63% 2.42% 1.21% 0.040% 0.015% 15.0% 15.00% 7.50% 5.00% 3.75% 2.50% 1.25% 0.04% 0.02% 15.5% 15.50% 7.75% 5.17% 3.88% 2.58% 1.29% 0.043% 0.016% 16.0% 16.00% 8.00% 5.33% 4.00% 2.67% 1.33% 0.044% 0.016% 16.5% 16.50% 8.25% 5.50% 4.13% 2.75% 1.38% 0.046% 0.017% 17.0% 17.00% 8.50% 5.67% 4.25% 2.83% 1.42% 0.047% 0.017% 17.5% 17.50% 8.75% 5.83% 4.38% 2.92% 1.46% 0.049% 0.018% 18.0% 18.00% 9.00% 6.00% 4.50% 3.00% 1.50% 0.050% 0.018% 18.5% 18.50% 9.25% 6.17% 4.63% 3.08% 1.54% 0.051% 0.019% 19.0% 19.00% 9.50% 6.33% 4.75% 3.17% 1.58% 0.053% 0.019% 19.5% 19.50% 9.75% 6.50% 4.88% 3.25% 1.63% 0.054% 0.020% 20.0% 20.00% 10.00% 6.67% 5.00% 3.33% 1.67% 0.06% 0.02% 20.5% 20.50% 10.25% 6.83% 5.13% 3.42% 1.71% 0.057% 0.021% 21.0% 21.00% 10.50% 7.00% 5.25% 3.50% 1.75% 0.058% 0.021% 21.5% 21.50% 10.75% 7.17% 5.38% 3.58% 1.79% 0.060% 0.022% 22.0% 22.00% 11.00% 7.33% 5.50% 3.67% 1.83% 0.061% 0.022% 22.5% 22.50% 11.25% 7.50% 5.63% 3.75% 1.88% 0.063% 0.023% 23.0% 23.00% 11.50% 7.67% 5.75% 3.83% 1.92% 0.064% 0.023% 23.5% 23.50% 11.75% 7.83% 5.88% 3.92% 1.96% 0.065% 0.024% 24.0% 24.00% 12.00% 8.00% 6.00% 4.00% 2.00% 0.067% 0.024% 24.5% 24.50% 12.25% 8.17% 6.13% 4.08% 2.04% 0.068% 0.025% 25.0% 25.00% 12.50% 8.33% 6.25% 4.17% 2.08% 0.07% 0.03% TASA EFECTIVA PERIODICA i(m), EN FUNCION DE LA TASA NOMINAL j(m)
  9. 9. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 9 m Año Semestre Cuatrimestre trimestre bimestre mes dia continuo i 1 2 3 4 6 12 360 1000 1.0% 1.00% 1.00% 1.00% 1.00% 1.00% 1.00% 0.995% 0.995% 1.5% 1.50% 1.49% 1.49% 1.49% 1.49% 1.49% 1.489% 1.489% 2.0% 2.00% 1.99% 1.99% 1.99% 1.98% 1.98% 1.980% 1.980% 2.5% 2.50% 2.48% 2.48% 2.48% 2.47% 2.47% 2.469% 2.469% 3.0% 3.00% 2.98% 2.97% 2.97% 2.96% 2.96% 2.956% 2.956% 3.5% 3.50% 3.47% 3.46% 3.45% 3.45% 3.45% 3.440% 3.440% 4.0% 4.00% 3.96% 3.95% 3.94% 3.93% 3.93% 3.922% 3.922% 4.5% 4.50% 4.45% 4.43% 4.43% 4.42% 4.41% 4.402% 4.402% 5.0% 5.00% 4.94% 4.92% 4.91% 4.90% 4.89% 4.879% 4.879% 5.5% 5.50% 5.43% 5.40% 5.39% 5.38% 5.37% 5.354% 5.354% 6.0% 6.00% 5.91% 5.88% 5.87% 5.86% 5.84% 5.827% 5.827% 6.5% 6.50% 6.40% 6.36% 6.35% 6.33% 6.31% 6.298% 6.298% 7.0% 7.00% 6.88% 6.84% 6.82% 6.80% 6.78% 6.767% 6.766% 7.5% 7.50% 7.36% 7.32% 7.30% 7.28% 7.25% 7.233% 7.232% 8.0% 8.00% 7.85% 7.80% 7.77% 7.75% 7.72% 7.697% 7.696% 8.5% 8.50% 8.33% 8.27% 8.24% 8.21% 8.19% 8.159% 8.158% 9.0% 9.00% 8.81% 8.74% 8.71% 8.68% 8.65% 8.619% 8.618% 9.5% 9.50% 9.28% 9.21% 9.18% 9.14% 9.11% 9.077% 9.076% 10.0% 10.00% 9.76% 9.68% 9.65% 9.61% 9.57% 9.532% 9.531% 10.5% 10.50% 10.24% 10.15% 10.11% 10.07% 10.03% 9.986% 9.985% 11.0% 11.00% 10.71% 10.62% 10.57% 10.53% 10.48% 10.438% 10.437% 11.5% 11.50% 11.19% 11.09% 11.03% 10.98% 10.93% 10.887% 10.886% 12.0% 12.00% 11.66% 11.55% 11.49% 11.44% 11.39% 11.335% 11.334% 12.5% 12.50% 12.13% 12.01% 11.95% 11.89% 11.84% 11.780% 11.779% 13.0% 13.00% 12.60% 12.47% 12.41% 12.35% 12.28% 12.224% 12.223% 13.5% 13.50% 13.07% 12.93% 12.87% 12.80% 12.73% 12.665% 12.664% 14.0% 14.00% 13.54% 13.39% 13.32% 13.25% 13.17% 13.105% 13.104% 14.5% 14.50% 14.01% 13.85% 13.77% 13.69% 13.62% 13.543% 13.541% 15.0% 15.00% 14.48% 14.31% 14.22% 14.14% 14.06% 13.979% 13.977% 15.5% 15.50% 14.94% 14.76% 14.67% 14.58% 14.50% 14.413% 14.411% 16.0% 16.00% 15.41% 15.22% 15.12% 15.03% 14.93% 14.845% 14.843% 16.5% 16.50% 15.87% 15.67% 15.57% 15.47% 15.37% 15.275% 15.273% 17.0% 17.00% 16.33% 16.12% 16.01% 15.91% 15.80% 15.704% 15.702% 17.5% 17.50% 16.79% 16.57% 16.46% 16.35% 16.24% 16.130% 16.128% 18.0% 18.00% 17.26% 17.02% 16.90% 16.78% 16.67% 16.555% 16.553% 18.5% 18.50% 17.72% 17.46% 17.34% 17.22% 17.09% 16.978% 16.976% 19.0% 19.00% 18.17% 17.91% 17.78% 17.65% 17.52% 17.400% 17.397% 19.5% 19.50% 18.63% 18.35% 18.22% 18.08% 17.95% 17.819% 17.816% 20.0% 20.00% 19.09% 18.80% 18.65% 18.51% 18.37% 18.237% 18.234% 20.5% 20.50% 19.54% 19.24% 19.09% 18.94% 18.79% 18.653% 18.650% 21.0% 21.00% 20.00% 19.68% 19.52% 19.37% 19.21% 19.067% 19.064% 21.5% 21.50% 20.45% 20.12% 19.96% 19.79% 19.63% 19.480% 19.476% 22.0% 22.00% 20.91% 20.56% 20.39% 20.22% 20.05% 19.891% 19.887% 22.5% 22.50% 21.36% 21.00% 20.82% 20.64% 20.47% 20.300% 20.296% 23.0% 23.00% 21.81% 21.43% 21.25% 21.06% 20.88% 20.707% 20.704% 23.5% 23.50% 22.26% 21.87% 21.67% 21.48% 21.29% 21.113% 21.109% 24.0% 24.00% 22.71% 22.30% 22.10% 21.90% 21.71% 21.518% 21.513% 24.5% 24.50% 23.16% 22.73% 22.52% 22.32% 22.11% 21.920% 21.916% 25.0% 25.00% 23.61% 23.17% 22.95% 22.73% 22.52% 22.32% 22.32% TASA NOMINAL j(m), EN FUNCION DE LA TASA EFECTIVA ANUAL i=(a)
  10. 10. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 10
  11. 11. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 11 FACTORES DE CALCULO FINANCIERO
  12. 12. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 12 1%1.00%2%2.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.01000.99011.000001.00001.010000.99010.00000.000011.02000.98041.000001.00001.020000.98040.00000.0000 21.02010.98030.497512.01000.507511.97040.98030.497521.04040.96120.495052.02000.515051.94160.96120.4950 31.03030.97060.330023.03010.340022.94102.92150.993431.06120.94230.326753.06040.346752.88392.84580.9868 41.04060.96100.246284.06040.256283.90205.80441.487641.08240.92380.242624.12160.262623.80775.61731.4752 51.05100.95150.196045.10100.206044.85349.61031.980151.10410.90570.192165.20400.212164.71359.24031.9604 61.06150.94200.162556.15200.172555.795514.32052.471061.12620.88800.158536.30810.178535.601413.68012.4423 71.07210.93270.138637.21350.148636.728219.91682.960271.14870.87060.134517.43430.154516.472018.90352.9208 81.08290.92350.120698.28570.130697.651726.38123.447881.17170.85350.116518.58300.136517.325524.87793.3961 91.09370.91430.106749.36850.116748.566033.69593.933791.19510.83680.102529.75460.122528.162231.57203.8681 101.10460.90530.0955810.46220.105589.4713041.84354.4179101.21900.82030.0913310.94970.111338.9825938.95514.3367 111.11570.89630.0864511.56680.0964510.367650.80674.9005111.24340.80430.0821812.16870.102189.786846.99774.8021 121.12680.88740.0788512.68250.0888511.255160.56875.3815121.26820.78850.0745613.41210.0945610.575355.67125.2642 131.13810.87870.0724113.80930.0824112.133771.11265.8607131.29360.77300.0681214.68030.0881211.348464.94755.7231 141.14950.87000.0669014.94740.0769013.003782.42216.3384141.31950.75790.0626015.97390.0826012.106274.79996.1786 151.16100.86130.0621216.09690.0721213.865194.48106.8143151.34590.74300.0578317.29340.0778312.849385.20216.6309 161.17260.85280.0579417.25790.0679414.7179107.27347.2886161.37280.72840.0536518.63930.0736513.577796.12887.0799 171.18430.84440.0542618.43040.0642615.5623120.78347.7613171.40020.71420.0499720.01210.0699714.2919107.55547.5256 181.19610.83600.0509819.61470.0609816.3983134.99578.2323181.42820.70020.0467021.41230.0667014.9920119.45817.9681 191.20810.82770.0480520.81090.0580517.2260149.89508.7017191.45680.68640.0437822.84060.0637815.6785131.81398.4073 201.22020.81950.0454222.01900.0554218.04555165.46649.1694201.48590.67300.0411624.29740.0611616.35143144.60038.8433 211.23240.81140.0430323.23920.0530318.8570181.69509.6354211.51570.65980.0387825.78330.0587817.0112157.79599.2760 221.24470.80340.0408624.47160.0508619.6604198.566310.0998221.54600.64680.0366327.29900.0566317.6580171.37959.7055 231.25720.79540.0388925.71630.0488920.4558216.066010.5626231.57690.63420.0346728.84500.0546718.2922185.330910.1317 241.26970.78760.0370726.97350.0470721.2434234.180011.0237241.60840.62170.0328730.42190.0528718.9139199.630510.5547 251.28240.77980.0354128.24320.0454122.0232252.894511.4831251.64060.60950.0312232.03030.0512219.5235214.259210.9745 261.29530.77200.0338729.52560.0438722.7952272.195711.9409261.67340.59760.0297033.67090.0497020.1210229.198711.3910 271.30820.76440.0324530.82090.0424523.5596292.070212.3971271.70690.58590.0282935.34430.0482920.7069244.431111.8043 281.32130.75680.0311232.12910.0411224.3164312.504712.8516281.74100.57440.0269937.05120.0469921.2813259.939212.2145 291.33450.74930.0299033.45040.0399025.0658333.486313.3044291.77580.56310.0257838.79220.0457821.8444275.706412.6214 301.34780.74190.0287534.78490.0387525.80771355.002113.7557301.81140.55210.0246540.56810.0446522.39646291.716413.0251 311.36130.73460.0276836.13270.0376826.5423377.039414.2052311.84760.54120.0236042.37940.0436022.9377307.953813.4257 321.37490.72730.0266737.49410.0366727.2696399.585814.6532321.88450.53060.0226144.22700.0426123.4683324.403513.8230 331.38870.72010.0257338.86900.0357327.9897422.629115.0995331.92220.52020.0216946.11160.0416923.9886341.050814.2172 341.40260.71300.0248440.25770.0348428.7027446.157215.5441341.96070.51000.0208248.03380.0408224.4986357.881714.6083 351.41660.70590.0240041.66030.0340029.4086470.158315.9871351.99990.50000.0200049.99450.0400024.9986374.882614.9961 361.43080.69890.0232143.07690.0332130.1075494.620716.4285362.03990.49020.0192351.99440.0392325.4888392.040515.3809 371.44510.69200.0224744.50760.0324730.7995519.532916.8682372.08070.48060.0185154.03430.0385125.9695409.342415.7625 381.45950.68520.0217645.95270.0317631.4847544.883517.3063382.12230.47120.0178256.11490.0378226.4406426.776416.1409 391.47410.67840.0210947.41230.0310932.1630570.661617.7428392.16470.46190.0171758.23720.0371726.9026444.330416.5163 401.48890.67170.0204648.88640.0304632.8347596.856118.1776402.20800.45290.0165660.40200.0365627.3555461.993116.8885 481.610.62030.0163361.220.0263337.9740820.1521.5976482.590.38650.0126079.350.0326030.6731605.965719.7556 541.710.58430.0140671.140.0240641.56871,001.5724.0945542.910.34320.0104595.670.0304532.8383715.181521.7789 601.820.55040.0122481.670.0222444.95501,192.8126.5333603.280.30480.00877114.050.0287734.7609823.697523.6961 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  13. 13. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 13 3%3.00%4%4.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.03000.97091.000001.00001.030000.97090.00000.000011.04000.96151.000001.00001.040000.96150.00000.0000 21.06090.94260.492612.03000.522611.91350.94260.492621.08160.92460.490202.04000.530201.88610.92460.4902 31.09270.91510.323533.09090.353532.82862.77290.980331.12490.88900.320353.12160.360352.77512.70250.9739 41.12550.88850.239034.18360.269033.71715.43831.463141.16990.85480.235494.24650.275493.62995.26701.4510 51.15930.86260.188355.30910.218354.57978.88881.940951.21670.82190.184635.41630.224634.45188.55471.9216 61.19410.83750.154606.46840.184605.417213.07622.413861.26530.79030.150766.63300.190765.242112.50622.3857 71.22990.81310.130517.66250.160516.230317.95472.881971.31590.75990.126617.89830.166616.002117.06572.8433 81.26680.78940.112468.89230.142467.019723.48063.345081.36860.73070.108539.21420.148536.732722.18063.2944 91.30480.76640.0984310.15910.128437.786129.61193.803291.42330.70260.0944910.58280.134497.435327.80133.7391 101.34390.74410.0872311.46390.117238.5302036.30884.2565101.48020.67560.0832912.00610.123298.1109033.88144.1773 111.38420.72240.0780812.80780.108089.252643.53304.7049111.53950.64960.0741513.48640.114158.760540.37724.6090 121.42580.70140.0704614.19200.100469.954051.24825.1485121.60100.62460.0665515.02580.106559.385147.24775.0343 131.46850.68100.0640315.61780.0940310.635059.41965.5872131.66510.60060.0601416.62680.100149.985654.45465.4533 141.51260.66110.0585317.08630.0885311.296168.01416.0210141.73170.57750.0546718.29190.0946710.563161.96185.8659 151.55800.64190.0537718.59890.0837711.937977.00026.4500151.80090.55530.0499420.02360.0899411.118469.73556.2721 161.60470.62320.0496120.15690.0796112.561186.34776.8742161.87300.53390.0458221.82450.0858211.652377.74416.6720 171.65280.60500.0459521.76160.0759513.166196.02807.2936171.94790.51340.0422023.69750.0822012.165785.95817.0656 181.70240.58740.0427123.41440.0727113.7535106.01377.7081182.02580.49360.0389925.64540.0789912.659394.34987.4530 191.75350.57030.0398125.11690.0698114.3238116.27888.1179192.10680.47460.0361427.67120.0761413.1339102.89337.8342 201.80610.55370.0372226.87040.0672214.87747126.79878.5229202.19110.45640.0335829.77810.0735813.59033111.56478.2091 211.86030.53750.0348728.67650.0648715.4150137.54968.9231212.27880.43880.0312831.96920.0712814.0292120.34148.5779 221.91610.52190.0327530.53680.0627515.9369148.50949.3186222.36990.42200.0292034.24800.0692014.4511129.20248.9407 231.97360.50670.0308132.45290.0608116.4436159.65669.7093232.46470.40570.0273136.61790.0673114.8568138.12849.2973 242.03280.49190.0290534.42650.0590516.9355170.971110.0954242.56330.39010.0255939.08260.0655915.2470147.10129.6479 252.09380.47760.0274336.45930.0574317.4131182.433610.4768252.66580.37510.0240141.64590.0640115.6221156.10409.9925 262.15660.46370.0259438.55300.0559417.8768194.026010.8535262.77250.36070.0225744.31170.0625715.9828165.121210.3312 272.22130.45020.0245640.70960.0545618.3270205.730911.2255272.88340.34680.0212447.08420.0612416.3296174.138510.6640 282.28790.43710.0232942.93090.0532918.7641217.532011.5930282.99870.33350.0200149.96760.0600116.6631183.142410.9909 292.35660.42430.0221145.21890.0521119.1885229.413711.9558293.11870.32070.0188852.96630.0588816.9837192.120611.3120 302.42730.41200.0210247.57540.0510219.60044241.361312.3141303.24340.30830.0178356.08490.0578317.29203201.061811.6274 312.50010.40000.0200050.00270.0500020.0004253.360912.6678313.37310.29650.0168659.32830.0568617.5885209.955611.9371 322.57510.38830.0190552.50280.0490520.3888265.399313.0169323.50810.28510.0159562.70150.0559517.8736218.792412.2411 332.65230.37700.0181655.07780.0481620.7658277.464213.3616333.64840.27410.0151066.20950.0551018.1476227.563412.5396 342.73190.36600.0173257.73020.0473221.1318289.543713.7018343.79430.26360.0143169.85790.0543118.4112236.260712.8324 352.81390.35540.0165460.46210.0465421.4872301.626714.0375353.94610.25340.0135873.65220.0535818.6646244.876813.1198 362.89830.34500.0158063.27590.0458021.8323313.702814.3688364.10390.24370.0128977.59830.0528918.9083253.405213.4018 372.98520.33500.0151166.17420.0451122.1672325.762214.6957374.26810.23430.0122481.70220.0522419.1426261.839913.6784 383.07480.32520.0144669.15940.0444622.4925337.795615.0182384.43880.22530.0116385.97030.0516319.3679270.175413.9497 393.16700.31580.0138472.23420.0438422.8082349.794215.3363394.61640.21660.0110690.40910.0510619.5845278.407014.2157 403.26200.30660.0132675.40130.0432623.1148361.749915.6502404.80100.20830.0105295.02550.0505219.7928286.530314.4765 484.130.24200.00958104.410.0395825.2667455.0318.0089486.570.15220.00718139.260.0471821.1951347.244616.3832 544.930.20270.00763131.140.0376326.5777521.1219.6073548.310.12030.00547182.850.0454721.9930387.443617.6167 605.890.16970.00613163.050.0361327.6756583.0521.06746010.520.09510.00420237.990.0442022.6235422.996618.6972 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  14. 14. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 14 5%5.00%6%6.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.05000.95241.000001.00001.050000.95240.00000.000011.06000.94341.000001.00001.060000.94340.00000.0000 21.10250.90700.487802.05000.537801.85940.90700.487821.12360.89000.485442.06000.545441.83340.89000.4854 31.15760.86380.317213.15250.367212.72322.63470.967531.19100.83960.314113.18360.374112.67302.56920.9612 41.21550.82270.232014.31010.282013.54605.10281.439141.26250.79210.228594.37460.288593.46514.94551.4272 51.27630.78350.180975.52560.230974.32958.23691.902551.33820.74730.177405.63710.237404.21247.93451.8836 61.34010.74620.147026.80190.197025.075711.96802.357961.41850.70500.143366.97530.203364.917311.45942.3304 71.40710.71070.122828.14200.172825.786416.23212.805271.50360.66510.119148.39380.179145.582415.44972.7676 81.47750.67680.104729.54910.154726.463220.97003.244581.59380.62740.101049.89750.161046.209819.84163.1952 91.55130.64460.0906911.02660.140697.107826.12683.675891.68950.59190.0870211.49130.147026.801724.57683.6133 101.62890.61390.0795012.57790.129507.7217331.65204.0991101.79080.55840.0758713.18080.135877.3600929.60234.0220 111.71030.58470.0703914.20680.120398.306437.49884.5144111.89830.52680.0667914.97160.126797.886934.87024.4213 121.79590.55680.0628315.91710.112838.863343.62414.9219122.01220.49700.0592816.86990.119288.383840.33694.8113 131.88560.53030.0564617.71300.106469.393649.98795.3215132.13290.46880.0529618.88210.112968.852745.96295.1920 141.97990.50510.0510219.59860.101029.898656.55385.7133142.26090.44230.0475821.01510.107589.295051.71285.5635 152.07890.48100.0463421.57860.0963410.379763.28806.0973152.39660.41730.0429623.27600.102969.712257.55465.9260 162.18290.45810.0422723.65750.0922710.837870.15976.4736162.54040.39360.0389525.67250.0989510.105963.45926.2794 172.29200.43630.0387025.84040.0887011.274177.14056.8423172.69280.37140.0354428.21290.0954410.477369.40116.6240 182.40660.41550.0355528.13240.0855511.689684.20437.2034182.85430.35030.0323630.90570.0923610.827675.35696.9597 192.52700.39570.0327530.53900.0827512.085391.32757.5569193.02560.33050.0296233.76000.0896211.158181.30627.2867 202.65330.37690.0302433.06600.0802412.4622198.48847.9030203.20710.31180.0271836.78560.0871811.4699287.23047.6051 212.78600.35890.0280035.71930.0780012.8212105.66738.2416213.39960.29420.0250039.99270.0850011.764193.11367.9151 222.92530.34180.0259738.50520.0759713.1630112.84618.5730223.60350.27750.0230543.39230.0830512.041698.94128.2166 233.07150.32560.0241441.43050.0741413.4886120.00878.8971233.81970.26180.0212846.99580.0812812.3034104.70078.5099 243.22510.31010.0224744.50200.0724713.7986127.14029.2140244.04890.24700.0196850.81560.0796812.5504110.38128.7951 253.38640.29530.0209547.72710.0709514.0939134.22759.5238254.29190.23300.0182354.86450.0782312.7834115.97329.0722 263.55570.28120.0195651.11350.0695614.3752141.25859.8266264.54940.21980.0169059.15640.0769013.0032121.46849.3414 273.73350.26780.0182954.66910.0682914.6430148.222610.1224274.82230.20740.0157063.70580.0757013.2105126.86009.6029 283.92010.25510.0171258.40260.0671214.8981155.110110.4114285.11170.19560.0145968.52810.0745913.4062132.14209.8568 294.11610.24290.0160562.32270.0660515.1411161.912610.6936295.41840.18460.0135873.63980.0735813.5907137.309610.1032 304.32190.23140.0150566.43880.0650515.37245168.622610.9691305.74350.17410.0126579.05820.0726513.76483142.358810.3422 314.53800.22040.0141370.76080.0641315.5928175.233311.2381316.08810.16430.0117984.80170.0717913.9291147.286410.5740 324.76490.20990.0132875.29880.0632815.8027181.739211.5005326.45340.15500.0110090.88980.0710014.0840152.090110.7988 335.00320.19990.0124980.06380.0624916.0025188.135111.7566336.84060.14620.0102797.34320.0702714.2302156.768111.0166 345.25330.19040.0117685.06700.0617616.1929194.416812.0063347.25100.13790.00960104.18380.0696014.3681161.319211.2276 355.51600.18130.0110790.32030.0610716.3742200.580712.2498357.68610.13010.00897111.43480.0689714.4982165.742711.4319 365.79180.17270.0104395.83630.0604316.5469206.623712.4872368.14730.12270.00839119.12090.0683914.6210170.038711.6298 376.08140.16440.00984101.62810.0598416.7113212.543412.7186378.63610.11580.00786127.26810.0678614.7368174.207211.8213 386.38550.15660.00928107.70950.0592816.8679218.337812.9440389.15430.10920.00736135.90420.0673614.8460178.249012.0065 396.70480.14910.00876114.09500.0587617.0170224.005413.1636399.70350.10310.00689145.05850.0668914.9491182.165212.1857 407.04000.14200.00828120.79980.0582817.1591229.545213.37754010.28570.09720.00646154.76200.0664615.0463185.956812.3590 4810.400.09610.00532188.030.0553218.0772269.2514.89434816.390.06100.00390256.560.0639015.6500212.035113.5485 5413.940.07170.00386258.770.0538618.5651293.8215.82655423.260.04300.00270370.920.0627015.9500227.131614.2402 6018.680.05350.00283353.580.0528318.9293314.3416.60626032.990.03030.00188533.130.0618816.1614239.042814.7909 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  15. 15. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 15 7%7.00%8%8.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.07000.93461.000001.00001.070000.93460.00000.000011.08000.92591.000001.00001.080000.92590.00000.0000 21.14490.87340.483092.07000.553091.80800.87340.483121.16640.85730.480772.08000.560771.78330.85730.4808 31.22500.81630.311053.21490.381052.62432.50600.954931.25970.79380.308033.24640.388032.57712.44500.9487 41.31080.76290.225234.43990.295233.38724.79471.415541.36050.73500.221924.50610.301923.31214.65011.4040 51.40260.71300.173895.75070.243894.10027.64671.865051.46930.68060.170465.86660.250463.99277.37241.8465 61.50070.66630.139807.15330.209804.766510.97842.303261.58690.63020.136327.33590.216324.622910.52332.2763 71.60580.62270.115558.65400.185555.389314.71492.730471.71380.58350.112078.92280.192075.206414.02422.6937 81.71820.58200.0974710.25980.167475.971318.78893.146581.85090.54030.0940110.63660.174015.746617.80613.0985 91.83850.54390.0834911.97800.153496.515223.14043.551791.99900.50020.0800812.48760.160086.246921.80813.4910 101.96720.50830.0723813.81640.142387.0235827.71563.9461102.15890.46320.0690314.48660.149036.7100825.97683.8713 112.10490.47510.0633615.78360.133367.498732.46654.3296112.33160.42890.0600816.64550.140087.139030.26574.2395 122.25220.44400.0559017.88850.125907.942737.35064.7025122.51820.39710.0527018.97710.132707.536134.63394.5957 132.40980.41500.0496520.14060.119658.357742.33025.0648132.71960.36770.0465221.49530.126527.903839.04634.9402 142.57850.38780.0443422.55050.114348.745547.37185.4167142.93720.34050.0413024.21490.121308.244243.47235.2731 152.75900.36240.0397925.12900.109799.107952.44615.7583153.17220.31520.0368327.15210.116838.559547.88575.5945 162.95220.33870.0358627.88810.105869.446657.52716.0897163.42590.29190.0329830.32430.112988.851452.26405.9046 173.15880.31660.0324330.84020.102439.763262.59236.4110173.70000.27030.0296333.75020.109639.121656.58836.2037 183.37990.29590.0294133.99900.0994110.059167.62196.7225183.99600.25020.0267037.45020.106709.371960.84266.4920 193.61650.27650.0267537.37900.0967510.335672.59917.0242194.31570.23170.0241341.44630.104139.603665.01346.7697 203.86970.25840.0243940.99550.0943910.5940177.50917.3163204.66100.21450.0218545.76200.101859.8181569.08987.0369 214.14060.24150.0222944.86520.0922910.835582.33937.5990215.03380.19870.0198350.42290.0998310.016873.06297.2940 224.43040.22570.0204149.00570.0904111.061287.07937.8725225.43650.18390.0180355.45680.0980310.200776.92577.5412 234.74050.21090.0187153.43610.0887111.272291.72018.1369235.87150.17030.0164260.89330.0964210.371180.67267.7786 245.07240.19710.0171958.17670.0871911.469396.25458.3923246.34120.15770.0149866.76480.0949810.528884.29978.0066 255.42740.18420.0158163.24900.0858111.6536100.67658.6391256.84850.14600.0136873.10590.0936810.674887.80418.2254 265.80740.17220.0145668.67650.0845611.8258104.98148.8773267.39640.13520.0125179.95440.0925110.810091.18428.4352 276.21390.16090.0134374.48380.0834311.9867109.16569.1072277.98810.12520.0114587.35080.0914510.935294.43908.6363 286.64880.15040.0123980.69770.0823912.1371113.22649.3289288.62710.11590.0104995.33880.0904911.051197.56878.8289 297.11430.14060.0114587.34650.0814512.2777117.16229.5427299.31730.10730.00962103.96590.0896211.1584100.57389.0133 307.61230.13140.0105994.46080.0805912.40904120.97189.74873010.06270.09940.00883113.28320.0888311.25778103.45589.1897 318.14510.12280.00980102.07300.0798012.5318124.65509.94713110.86770.09200.00811123.34590.0881111.3498106.21639.3584 328.71530.11470.00907110.21820.0790712.6466128.212010.13813211.73710.08520.00745134.21350.0874511.4350108.85759.5197 339.32530.10720.00841118.93340.0784112.7538131.643510.32193312.67600.07890.00685145.95060.0868511.5139111.38199.6737 349.97810.10020.00780128.25880.0778012.8540134.950710.49873413.69010.07300.00630158.62670.0863011.5869113.79249.8208 3510.67660.09370.00723138.23690.0772312.9477138.135310.66873514.78530.06760.00580172.31680.0858011.6546116.09209.9611 3611.42390.08750.00672148.91350.0767213.0352141.199010.83213615.96820.06260.00534187.10210.0853411.7172118.283910.0949 3712.22360.08180.00624160.33740.0762413.1170144.144110.98913717.24560.05800.00492203.07030.0849211.7752120.371310.2225 3813.07930.07650.00580172.56100.0758013.1935146.973011.13983818.62530.05370.00454220.31590.0845411.8289122.357910.3440 3913.99480.07150.00539185.64030.0753913.2649149.688311.28453920.11530.04970.00419238.94120.0841911.8786124.247010.4597 4014.97450.06680.00501199.63510.0750113.3317152.292811.42334021.72450.04600.00386259.05650.0838611.9246126.042210.5699 4825.730.03890.00283353.270.0728313.7305169.5012.34474840.210.02490.00204490.130.0820412.1891137.442811.2758 5438.610.02590.00186537.320.0718613.9157178.8212.85005463.810.01570.00127785.110.0812712.3041143.222911.6403 6057.950.01730.00123813.520.0712314.0392185.7713.232160101.260.00990.000801,253.210.0808012.3766147.300011.9015 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  16. 16. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 16 9%9.00%10%10.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.09000.91741.000001.00001.090000.91740.00000.000011.10000.90911.000001.00001.100000.90910.00000.0000 21.18810.84170.478472.09000.568471.75910.84170.478521.21000.82640.476192.10000.576191.73550.82640.4762 31.29500.77220.305053.27810.395052.53132.38600.942631.33100.75130.302113.31000.402112.48692.32910.9366 41.41160.70840.218674.57310.308673.23974.51131.392541.46410.68300.215474.64100.315473.16994.37811.3812 51.53860.64990.167095.98470.257093.88977.11101.828251.61050.62090.163806.10510.263803.79086.86181.8101 61.67710.59630.132927.52330.222924.485910.09242.249861.77160.56450.129617.71560.229614.35539.68422.2236 71.82800.54700.108699.20040.198695.033013.37462.657471.94870.51320.105419.48720.205414.868412.76312.6216 81.99260.50190.0906711.02850.180675.534816.88773.051282.14360.46650.0874411.43590.187445.334916.02873.0045 92.17190.46040.0768013.02100.166805.995220.57113.431292.35790.42410.0736413.57950.173645.759019.42153.3724 102.36740.42240.0658215.19290.155826.4176624.37283.7978102.59370.38550.0627515.93740.162756.1445722.89133.7255 112.58040.38750.0569517.56030.146956.805228.24814.1510112.85310.35050.0539618.53120.153966.495126.39634.0641 122.81270.35550.0496520.14070.139657.160732.15904.4910123.13840.31860.0467621.38430.146766.813729.90124.3884 133.06580.32620.0435722.95340.133577.486936.07314.8182133.45230.28970.0407824.52270.140787.103433.37724.6988 143.34170.29920.0384326.01920.128437.786239.96335.1326143.79750.26330.0357527.97500.135757.366736.80054.9955 153.64250.27450.0340629.36090.124068.060743.80695.4346154.17720.23940.0314731.77250.131477.606140.15205.2789 163.97030.25190.0303033.00340.120308.312647.58495.7245164.59500.21760.0278235.94970.127827.823743.41645.5493 174.32760.23110.0270536.97370.117058.543651.28216.0024175.05450.19780.0246640.54470.124668.021646.58195.8071 184.71710.21200.0242141.30130.114218.755654.88606.2687185.55990.17990.0219345.59920.121938.201449.63956.0526 195.14170.19450.0217346.01850.111738.950158.38686.5236196.11590.16350.0195551.15910.119558.364952.58276.2861 205.60440.17840.0195551.16010.109559.1285561.77706.7674206.72750.14860.0174657.27500.117468.5135655.40696.5081 216.10880.16370.0176256.76450.107629.292265.05097.0006217.40020.13510.0156264.00250.115628.648758.10956.7189 226.65860.15020.0159062.87330.105909.442468.20487.2232228.14030.12280.0140171.40270.114018.771560.68936.9189 237.25790.13780.0143869.53190.104389.580271.23597.4357238.95430.11170.0125779.54300.112578.883263.14627.1085 247.91110.12640.0130276.78980.103029.706674.14337.6384249.84970.10150.0113088.49730.111308.984765.48137.2881 258.62310.11600.0118184.70090.101819.822676.92657.83162510.83470.09230.0101798.34710.110179.077067.69647.4580 269.39920.10640.0107293.32400.100729.929079.58638.01562611.91820.08390.00916109.18180.109169.160969.79407.6186 2710.24510.09760.00973102.72310.0997310.026682.12418.19062713.11000.07630.00826121.09990.108269.237271.77737.7704 2811.16710.08950.00885112.96820.0988510.116184.54198.35712814.42100.06930.00745134.20990.107459.306673.64957.9137 2912.17220.08220.00806124.13540.0980610.198386.84228.51542915.86310.06300.00673148.63090.106739.369675.41468.0489 3013.26770.07540.00734136.30750.0973410.2736589.02808.66573017.44940.05730.00608164.49400.106089.4269177.07668.1762 3114.46180.06910.00669149.57520.0966910.342891.10248.80833119.19430.05210.00550181.94340.105509.479078.63958.2962 3215.76330.06340.00610164.03700.0961010.406293.06908.94363221.11380.04740.00497201.13780.104979.526480.10788.4091 3317.18200.05820.00556179.80030.0955610.464494.93149.07183323.22520.04310.00450222.25150.104509.569481.48568.5152 3418.72840.05340.00508196.98230.0950810.517896.69359.19333425.54770.03910.00407245.47670.104079.608682.77738.6149 3520.41400.04900.00464215.71080.0946410.566898.35909.30833528.10240.03560.00369271.02440.103699.644283.98728.7086 3622.25120.04490.00424236.12470.0942410.611899.93199.41713630.91270.03230.00334299.12680.103349.676585.11948.7965 3724.25380.04120.00387258.37590.0938710.6530101.41629.52003734.00390.02940.00303330.03950.103039.705986.17818.8789 3826.43670.03780.00354282.62980.0935410.6908102.81589.61723837.40430.02670.00275364.04340.102759.732787.16738.9562 3928.81600.03470.00324309.06650.0932410.7255104.13459.70903941.14480.02430.00249401.44780.102499.757088.09089.0285 4031.40940.03180.00296337.88240.0929610.7574105.37629.79574045.25930.02210.00226442.59260.102269.779188.95259.0962 4862.590.01600.00146684.280.0914610.9336112.9610.33174897.020.01030.00104960.170.101049.896994.02179.5001 54104.960.00950.000871,155.130.0908711.0053116.5610.591754171.870.00580.000591,708.720.100599.941896.27639.6840 60176.030.00570.000511,944.790.0905111.0480118.9710.768360304.480.00330.000333,034.820.100339.967297.70109.8023 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  17. 17. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 17 11%11.00%12%12.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.11000.90091.000001.00001.110000.90090.00000.000011.12000.89291.000001.00001.120000.89290.00000.0000 21.23210.81160.473932.11000.583931.71250.81160.473921.25440.79720.471702.12000.591701.69010.79720.4717 31.36760.73120.299213.34210.409212.44372.27400.930631.40490.71180.296353.37440.416352.40182.22080.9246 41.51810.65870.212334.70970.322333.10244.25021.370041.57350.63550.209234.77930.329233.03734.12731.3589 51.68510.59350.160576.22780.270573.69596.62401.792351.76230.56740.157416.35280.277413.60486.39701.7746 61.87040.53460.126387.91290.236384.23059.29722.197661.97380.50660.123238.11520.243234.11148.93022.1720 72.07620.48170.102229.78330.212224.712212.18722.586372.21070.45230.0991210.08900.219124.563811.64432.5515 82.30450.43390.0843211.85940.194325.146115.22462.958582.47600.40390.0813012.29970.201304.967614.47142.9131 92.55800.39090.0706014.16400.180605.537018.35203.314492.77310.36060.0676814.77570.187685.328217.35633.2574 102.83940.35220.0598016.72200.169805.8892321.52173.6544103.10580.32200.0569817.54870.176985.6502220.25413.5847 113.15180.31730.0511219.56140.161126.206524.69453.9788113.47850.28750.0484220.65460.168425.937723.12883.8953 123.49850.28580.0440322.71320.154036.492427.83884.2879123.89600.25670.0414424.13310.161446.194425.95234.1897 133.88330.25750.0381526.21160.148156.749930.92904.5822134.36350.22920.0356828.02910.155686.423528.70244.4683 144.31040.23200.0332330.09490.143236.981933.94494.8619144.88710.20460.0308732.39260.150876.628231.36244.7317 154.78460.20900.0290734.40540.139077.190936.87095.1275155.47360.18270.0268237.27970.146826.810933.92024.9803 165.31090.18830.0255239.18990.135527.379239.69535.3794166.13040.16310.0233942.75330.143396.974036.36705.2147 175.89510.16960.0224744.50080.132477.548842.40955.6180176.86600.14560.0204648.88370.140467.119638.69735.4353 186.54360.15280.0198450.39590.129847.701645.00745.8439187.69000.13000.0179455.74970.137947.249740.90805.6427 197.26330.13770.0175656.93950.127567.839347.48566.0574198.61280.11610.0157663.43970.135767.365842.99795.8375 208.06230.12400.0155864.20280.125587.9633349.84236.2590209.64630.10370.0138872.05240.133887.4694444.96766.0202 218.94920.11170.0138472.26510.123848.075152.07716.44912110.80380.09260.0122481.69870.132247.562046.81886.1913 229.93360.10070.0123181.21430.122318.175754.19126.62832212.10030.08260.0108192.50260.130817.644648.55436.3514 2311.02630.09070.0109791.14790.120978.266456.18646.79692313.55230.07380.00956104.60290.129567.718450.17766.5010 2412.23920.08170.00979102.17420.119798.348158.06566.95552415.17860.06590.00846118.15520.128467.784351.69296.6406 2513.58550.07360.00874114.41330.118748.421759.83227.10452517.00010.05880.00750133.33390.127507.843153.10466.7708 2615.07990.06630.00781127.99880.117818.488161.49007.24432619.04010.05250.00665150.33390.126657.895754.41776.8921 2716.73860.05970.00699143.07860.116998.547863.04337.37542721.32490.04690.00590169.37400.125907.942655.63697.0049 2818.57990.05380.00626159.81730.116268.601664.49657.49822823.88390.04190.00524190.69890.125247.984456.76747.1098 2920.62370.04850.00561178.39720.115618.650165.85427.61312926.74990.03740.00466214.58280.124668.021857.81417.2071 3022.89230.04370.00502199.02090.115028.6937967.12107.72063029.95990.03340.00414241.33270.124148.0551858.78217.2974 3125.41040.03940.00451221.91320.114518.733168.30167.82103133.55510.02980.00369271.29260.123698.085059.67617.3811 3228.20560.03550.00404247.32360.114048.768669.40077.91473237.58170.02660.00328304.84770.123288.111660.50107.4586 3331.30820.03190.00363275.52920.113638.800570.42288.00213342.09150.02380.00292342.42940.122928.135461.26127.5302 3434.75210.02880.00326306.83740.113268.829371.37248.08363447.14250.02120.00260384.52100.122608.156661.96127.5965 3538.57490.02590.00293341.58960.112938.855272.25388.15943552.79960.01890.00232431.66350.122328.175562.60527.6577 3642.81810.02340.00263380.16440.112638.878673.07128.23003659.13560.01690.00206484.46310.122068.192463.19707.7141 3747.52810.02100.00236422.98250.112368.899673.82868.29573766.23180.01510.00184543.59870.121848.207563.74067.7661 3852.75620.01900.00213470.51060.112138.918674.53008.35673874.17970.01350.00164609.83050.121648.221064.23947.8141 3958.55930.01710.00191523.26670.111918.935775.17898.41333983.08120.01200.00146684.01020.121468.233064.69677.8582 4065.00090.01540.00172581.82610.111728.951175.77898.46594093.05100.01070.00130767.09140.121308.243865.11597.8988 48149.800.00670.000741,352.700.110749.030279.188.768348230.390.00430.000521,911.590.120528.297267.40688.1241 54280.180.00360.000392,538.020.110399.058580.608.897554454.750.00220.000263,781.250.120268.315068.30228.2143 60524.060.00190.000214,755.070.110219.073681.458.976260897.600.00110.000137,471.640.120138.324068.81008.2664 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  18. 18. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 18 13%13.00%14%14.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.13000.88501.000001.00001.130000.88500.00000.000011.14000.87721.000001.00001.140000.87720.00000.0000 21.27690.78310.469482.13000.599481.66810.78310.469521.29960.76950.467292.14000.607291.64670.76950.4673 31.44290.69310.293523.40690.423522.36122.16920.918731.48150.67500.290733.43960.430732.32162.11940.9129 41.63050.61330.206194.84980.336192.97454.00921.347941.68900.59210.203204.92110.343202.91373.89571.3370 51.84240.54280.154316.48030.284313.51726.18021.757151.92540.51940.151286.61010.291283.43315.97311.7399 62.08200.48030.120158.32270.250153.99758.58182.146862.19500.45560.117168.53550.257163.88878.25112.1218 72.35260.42510.0961110.40470.226114.422611.13222.517172.50230.39960.0931910.73050.233194.288310.64892.4832 82.65840.37620.0783912.75730.208394.798813.76532.868582.85260.35060.0755713.23280.215574.638913.10282.8246 93.00400.33290.0648715.41570.194875.131716.42843.201493.25190.30750.0621716.08530.202174.946415.56293.1463 103.39460.29460.0542918.41970.184295.4262419.07973.5162103.70720.26970.0517119.33730.191715.2161217.99063.4490 113.83590.26070.0458421.81430.175845.686921.68673.8134114.22620.23660.0433923.04450.183395.452720.35673.7333 124.33450.23070.0389925.65020.168995.917624.22444.0936124.81790.20760.0366727.27070.176675.660322.63993.9998 134.89800.20420.0333529.98470.163356.121826.67444.3573135.49240.18210.0311632.08870.171165.842424.82474.2491 145.53480.18070.0286734.88270.158676.302529.02324.6050146.26130.15970.0266137.58110.166616.002126.90094.4819 156.25430.15990.0247440.41750.154746.462431.26174.8375157.13790.14010.0228143.84240.162816.142228.86234.6990 167.06730.14150.0214346.67170.151436.603933.38415.0552168.13720.12290.0196250.98040.159626.265130.70574.9011 177.98610.12520.0186153.73910.148616.729135.38765.2589179.27650.10780.0169259.11760.156926.372932.43055.0888 189.02430.11080.0162061.72510.146206.839937.27145.44911810.57520.09460.0146268.39410.154626.467434.03805.2630 1910.19740.09810.0141370.74940.144136.938039.03665.62651912.05570.08290.0126678.96920.152666.550435.53115.4243 2011.52310.08680.0123580.94680.142357.0247540.68545.79172013.74350.07280.0109991.02490.150996.6231336.91355.5734 2113.02110.07680.0108192.46990.140817.101642.22145.94542115.66760.06380.00954104.76840.149546.687038.19015.7111 2214.71380.06800.00948105.49100.139487.169543.64866.08812217.86100.05600.00830120.43600.148306.742939.36585.8381 2316.62660.06010.00832120.20480.138327.229744.97186.22052320.36160.04910.00723138.29700.147236.792140.44635.9549 2418.78810.05320.00731136.83150.137317.282946.19606.34312423.21220.04310.00630158.65860.146306.835141.43716.0624 2521.23050.04710.00643155.61960.136437.330047.32646.45662526.46190.03780.00550181.87080.145506.872942.34416.1610 2623.99050.04170.00565176.85010.135657.371748.36856.56142630.16660.03310.00480208.33270.144806.906143.17286.2514 2727.10930.03690.00498200.84060.134987.408649.32766.65822734.38990.02910.00419238.49930.144196.935243.92896.3342 2830.63350.03260.00439227.94990.134397.441250.20906.74742839.20450.02550.00366272.88920.143666.960744.61766.4100 2934.61580.02890.00387258.58340.133877.470151.01796.82962944.69310.02240.00320312.09370.143206.983045.24416.4791 3039.11590.02560.00341293.19920.133417.4956551.75926.90523050.95020.01960.00280356.78680.142807.0026645.81326.5423 3144.20100.02260.00301332.31510.133017.518352.43806.97473158.08320.01720.00245407.73700.142457.019946.32976.5998 3249.94710.02000.00266376.51610.132667.538353.05867.03853266.21480.01510.00215465.82020.142157.035046.79796.6522 3356.44020.01770.00234426.46320.132347.556053.62567.09713375.48490.01320.00188532.03500.141887.048247.22186.6998 3463.77740.01570.00207482.90340.132077.571754.14307.15073486.05280.01160.00165607.51990.141657.059947.60536.7431 3572.06850.01390.00183546.68080.131837.585654.61487.19983598.10020.01020.00144693.57270.141447.070047.95196.7824 3681.43740.01230.00162618.74930.131627.597955.04467.244836111.83420.00890.00126791.67290.141267.079048.26496.8180 3792.02430.01090.00143700.18670.131437.608755.43587.285837127.49100.00780.00111903.50710.141117.086848.54726.8503 38103.98740.00960.00126792.21100.131267.618355.79167.323338145.33970.00690.000971,030.99810.140977.093748.80186.8796 39117.50580.00850.00112896.19840.131127.626856.11507.357639165.68730.00600.000851,176.33780.140857.099749.03126.9060 40132.78160.00750.000991,013.70420.130997.634456.40877.388840188.88350.00530.000751,342.02510.140757.105049.23766.9300 48352.990.00280.000372,707.630.130377.670557.967.555948538.810.00190.000263,841.480.140267.129650.28947.0536 54734.910.00140.000185,645.480.130187.681858.537.6187541,182.670.00080.000128,440.470.140127.136850.65117.0972 601,530.050.00070.0000911,761.950.130097.687358.837.6531602,595.920.00040.0000518,535.130.140057.140150.83577.1197 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  19. 19. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 19 15%15.00%16%16.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.15000.86961.000001.00001.150000.86960.00000.000011.16000.86211.000001.00001.160000.86210.00000.0000 21.32250.75610.465122.15000.615121.62570.75610.465121.34560.74320.462962.16000.622961.60520.74320.4630 31.52090.65750.287983.47250.437982.28322.07120.907131.56090.64070.285263.50560.445262.24592.02450.9014 41.74900.57180.200274.99340.350272.85503.78641.326341.81060.55230.197385.06650.357382.79823.68141.3156 52.01140.49720.148326.74240.298323.35225.77511.722852.10030.47610.145416.87710.305413.27435.58581.7060 62.31310.43230.114248.75370.264243.78457.93682.097262.43640.41040.111398.97750.271393.68477.63802.0729 72.66000.37590.0903611.06680.240364.160410.19242.449872.82620.35380.0876111.41390.247614.03869.76102.4169 83.05900.32690.0728513.72680.222854.487312.48072.781383.27840.30500.0702214.24010.230224.343611.89622.7388 93.51790.28430.0595716.78580.209574.771614.75483.092293.80300.26300.0570817.51850.217084.606513.99983.0391 104.04560.24720.0492520.30370.199255.0187716.97953.3832104.41140.22670.0469021.32150.206904.8332316.03993.3187 114.65240.21490.0410724.34930.191075.233719.12893.6549115.11730.19540.0388625.73290.198865.028617.99413.5783 125.35030.18690.0344829.00170.184485.420621.18493.9082125.93600.16850.0324130.85020.192415.197119.84723.8189 136.15280.16250.0291134.35190.179115.583123.13524.1438136.88580.14520.0271836.78620.187185.342321.58994.0413 147.07570.14130.0246940.50470.174695.724524.97254.3624147.98750.12520.0229043.67200.182905.467523.21754.2464 158.13710.12290.0210247.58040.171025.847426.69304.5650159.26550.10790.0193651.65950.179365.575524.72844.4352 169.35760.10690.0179555.71750.167955.954228.29604.75221610.74800.09300.0164160.92500.176415.668526.12414.6086 1710.76130.09290.0153765.07510.165376.047229.78284.92511712.46770.08020.0139571.67300.173955.748727.40744.7676 1812.37550.08080.0131975.83640.163196.128031.15655.08431814.46250.06910.0118884.14070.171885.817828.58284.9130 1914.23180.07030.0113488.21180.161346.198232.42135.23071916.77650.05960.0101498.60320.170145.877529.65575.0457 2016.36650.06110.00976102.44360.159766.2593333.58225.36512019.46080.05140.00867115.37970.168675.9288430.63215.1666 2118.82150.05310.00842118.81010.158426.312534.64485.48832122.57450.04430.00742134.84050.167425.973131.51805.2766 2221.64470.04620.00727137.63160.157276.358735.61505.60102226.18640.03820.00635157.41500.166356.011332.32005.3765 2324.89150.04020.00628159.27640.156286.398836.49885.70402330.37620.03290.00545183.60140.165456.044233.04425.4671 2428.62520.03490.00543184.16780.155436.433837.30235.79792435.23640.02840.00467213.97760.164676.072633.69705.5490 2532.91900.03040.00470212.79300.154706.464138.03145.88342540.87420.02450.00401249.21400.164016.097134.28415.6230 2637.85680.02640.00407245.71200.154076.490638.69185.96122647.41410.02110.00345290.08830.163456.118234.81145.6898 2743.53530.02300.00353283.56880.153536.513539.28906.03192755.00040.01820.00296337.50240.162966.136435.28415.7500 2850.06560.02000.00306327.10410.153066.533539.82836.09602863.80040.01570.00255392.50280.162556.152035.70735.8041 2957.57550.01740.00265377.16970.152656.550940.31466.15412974.00850.01350.00219456.30320.162196.165636.08565.8528 3066.21180.01510.00230434.74510.152306.5659840.75266.20663085.84990.01160.00189530.31170.161896.1772036.42345.8964 3176.14350.01310.00200500.95690.152006.579141.14666.25413199.58590.01000.00162616.16160.161626.187236.72475.9356 3287.56510.01140.00173577.10050.151736.590541.50066.297032115.51960.00870.00140715.74750.161406.195936.99305.9706 33100.69980.00990.00150664.66550.151506.600541.81846.335733134.00270.00750.00120831.26710.161206.203437.23186.0019 34115.80480.00860.00131765.36540.151316.609142.10336.370534155.44320.00640.00104965.26980.161046.209837.44416.0299 35133.17550.00750.00113881.17020.151136.616642.35866.401935180.31410.00550.000891,120.71300.160896.215337.63276.0548 36153.15190.00650.000991,014.34570.150996.623142.58726.430136209.16430.00480.000771,301.02700.160776.220137.80006.0771 37176.12460.00570.000861,167.49750.150866.628842.79166.455437242.63060.00410.000661,510.19140.160666.224237.94846.0969 38202.54330.00490.000741,343.62220.150746.633842.97436.478138281.45150.00360.000571,752.82200.160576.227838.07996.1145 39232.92480.00430.000651,546.16550.150656.638043.13746.498539326.48380.00310.000492,034.27350.160496.230938.19636.1302 40267.86350.00370.000561,779.09030.150566.641843.28306.516840378.72120.00260.000422,360.75720.160426.233538.29926.1441 48819.400.00120.000185,456.000.150186.658544.006.6080481,241.610.00080.000137,753.780.160136.245038.78946.2113 541,895.320.00050.0000812,628.820.150086.663144.236.6382543,025.040.00030.0000518,900.260.160056.247938.93806.2321 604,384.000.00020.0000329,219.990.150036.665144.346.6530607,370.200.00010.0000246,057.510.160026.249239.00636.2419 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  20. 20. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 20 17%17.00%18%18.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.17000.85471.000001.00001.170000.85470.00000.000011.18000.84751.000001.00001.180000.84750.00000.0000 21.36890.73050.460832.17000.630831.58520.73050.460821.39240.71820.458722.18000.638721.56560.71820.4587 31.60160.62440.282573.53890.452572.20961.97930.895831.64300.60860.279923.57240.459922.17431.93540.8902 41.87390.53370.194535.14050.364532.74323.58021.305141.93880.51580.191745.21540.371742.69013.48281.2947 52.19240.45610.142567.01440.312563.19935.40461.689352.28780.43710.139787.15420.319783.12725.23121.6728 62.56520.38980.108619.20680.278613.58927.35382.048962.69960.37040.105919.44200.285913.49767.08342.0252 73.00120.33320.0849511.77200.254953.92249.35302.384573.18550.31390.0823612.14150.262363.81158.96702.3526 83.51150.28480.0676914.77330.237694.207211.34652.696983.75890.26600.0652415.32700.245244.077610.82922.6558 94.10840.24340.0546918.28470.224694.450613.29372.987094.43550.22550.0523919.08590.232394.303012.63292.9358 104.80680.20800.0446622.39310.214664.6586015.16613.2555105.23380.19110.0425123.52130.222514.4940914.35253.1936 115.62400.17780.0367627.19990.206764.836416.94423.5035116.17590.16190.0347828.75510.214784.656015.97163.4303 126.58010.15200.0304732.82390.200474.988418.61593.7318127.28760.13720.0286334.93110.208634.793217.48113.6470 137.69870.12990.0253839.40400.195385.118320.17463.9417138.59940.11630.0236942.21870.203694.909518.87653.8449 149.00750.11100.0212347.10270.191235.229321.61784.13401410.14720.09850.0196850.81800.199685.008120.15764.0250 1510.53870.09490.0178256.11010.187825.324222.94634.30981511.97370.08350.0164060.96530.196405.091621.32694.1887 1612.33030.08110.0150066.64880.185005.405324.16284.47021614.12900.07080.0137172.93900.193715.162422.38854.3369 1714.42650.06930.0126678.97920.182665.474625.27194.61621716.67220.06000.0114987.06800.191495.222323.34824.4708 1816.87900.05920.0107193.40560.180715.533926.27904.74881819.67330.05080.00964103.74030.189645.273224.21234.5916 1919.74840.05060.00907110.28460.179075.584527.19054.86891923.21440.04310.00810123.41350.188105.316224.98774.7003 2023.10560.04330.00769130.03290.177695.6277728.01284.97762027.39300.03650.00682146.62800.186825.3527525.68134.7978 2127.03360.03700.00653153.13850.176535.664828.75265.07572132.32380.03090.00575174.02100.185755.383726.30004.8851 2231.62930.03160.00555180.17210.175555.696429.41665.16412238.14210.02620.00485206.34480.184855.409926.85064.9632 2337.00620.02700.00472211.80130.174725.723430.01115.24362345.00760.02220.00409244.48680.184095.432127.33945.0329 2443.29730.02310.00402248.80760.174025.746530.54235.31492453.10900.01880.00345289.49450.183455.450927.77255.0950 2550.65780.01970.00342292.10490.173425.766231.01605.37892562.66860.01600.00292342.60350.182925.466928.15555.1502 2659.26970.01690.00292342.76270.172925.783131.43785.43622673.94900.01350.00247405.27210.182475.480428.49355.1991 2769.34550.01440.00249402.03230.172495.797531.81285.48732787.25980.01150.00209479.22110.182095.491928.79155.2425 2881.13420.01230.00212471.37780.172125.809932.14565.532928102.96660.00970.00177566.48090.181775.501629.05375.2810 2994.92710.01050.00181552.51210.171815.820432.44055.573629121.50050.00820.00149669.44750.181495.509829.28425.3149 30111.06470.00900.00154647.43910.171545.8293932.70165.609830143.37060.00700.00126790.94800.181265.5168129.48645.3448 31129.94560.00770.00132758.50380.171325.837132.93255.641931169.17740.00590.00107934.31860.181075.522729.66385.3712 32152.03640.00660.00113888.44940.171135.843733.13645.670532199.62930.00500.000911,103.49600.180915.527729.81915.3945 33177.88260.00560.000961,040.48580.170965.849333.31635.695833235.56250.00420.000771,303.12530.180775.532029.95495.4149 34208.12260.00480.000821,218.36840.170825.854133.47485.718234277.96380.00360.000651,538.68780.180655.535630.07365.4328 35243.50350.00410.000701,426.49100.170705.858233.61455.738035327.99730.00300.000551,816.65160.180555.538630.17735.4485 36284.89910.00350.000601,669.99450.170605.861733.73735.755536387.03680.00260.000472,144.64890.180475.541230.26775.4623 37333.33190.00300.000511,954.89360.170515.864733.84535.771037456.70340.00220.000392,531.68570.180395.543430.34655.4744 38389.99830.00260.000442,288.22550.170445.867333.94025.784738538.91000.00190.000332,988.38910.180335.545230.41525.4849 39456.29800.00220.000372,678.22380.170375.869534.02355.796739635.91390.00160.000283,527.29920.180285.546830.47495.4941 40533.86870.00190.000323,134.52180.170325.871334.09655.807340750.37830.00130.000244,163.21300.180245.548230.52695.5022 481,874.660.00050.0000911,021.500.170095.879234.435.8567482,820.570.00040.0000615,664.260.180065.553630.75875.5385 544,808.800.00020.0000428,281.160.170045.881134.535.8711547,614.270.00010.0000242,295.960.180025.554830.82075.5485 6012,335.360.00010.0000172,555.040.170015.881934.575.87756020,555.140.00000.00001114,189.670.180015.555330.84655.5526 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  21. 21. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 21 19%19.00%20%20.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.19000.84031.000001.00001.190000.84030.00000.000011.20000.83331.000001.00001.200000.83330.00000.0000 21.41610.70620.456622.19000.646621.54650.70620.456621.44000.69440.454552.20000.654551.52780.69440.4545 31.68520.59340.277313.60610.467312.13991.89300.884631.72800.57870.274733.64000.474732.10651.85190.8791 42.00530.49870.188995.29130.378992.63863.38901.284442.07360.48230.186295.36800.386292.58873.29861.2742 52.38640.41900.137057.29660.327053.05765.06521.656652.48830.40190.134387.44160.334382.99064.90611.6405 62.83980.35210.103279.68300.293273.40986.82592.001962.98600.33490.100719.92990.300713.32556.58061.9788 73.37930.29590.0798512.52270.269853.70578.60142.321173.58320.27910.0774212.91590.277423.60468.25512.2902 84.02140.24870.0628915.90200.252893.954410.34212.615484.29980.23260.0606116.49910.260613.83729.88312.5756 94.78540.20900.0501919.92340.240194.163312.01382.885695.15980.19380.0480820.79890.248084.031011.43352.8364 105.69470.17560.0404724.70890.230474.3389313.59433.1331106.19170.16150.0385225.95870.238524.1924712.88713.0739 116.77670.14760.0328930.40350.222894.486515.06993.3589117.43010.13460.0311032.15040.231104.327114.23303.2893 128.06420.12400.0269037.18020.216904.610516.43403.5645128.91610.11220.0252639.58050.225264.439215.46673.4841 139.59640.10420.0221045.24450.212104.714717.68443.75091310.69930.09350.0206248.49660.220624.532716.58833.6597 1411.41980.08760.0182354.84090.208234.802318.82283.91961412.83920.07790.0168959.19590.216894.610617.60083.8175 1513.58950.07360.0150966.26070.205094.875919.85304.07171515.40700.06490.0138872.03510.213884.675518.50953.9588 1616.17150.06180.0125279.85020.202524.937720.78064.20861618.48840.05410.0114487.44210.211444.729619.32084.0851 1719.24410.05200.0104196.02180.200414.989721.61204.33141722.18610.04510.00944105.93060.209444.774620.04194.1976 1822.90050.04370.00868115.26590.198685.033322.35434.44131826.62330.03760.00781128.11670.207814.812220.68054.2975 1927.25160.03670.00724138.16640.197245.070023.01484.53941931.94800.03130.00646154.74000.206464.843521.24394.3861 2032.42940.03080.00605165.41800.196055.1008623.60074.62682038.33760.02610.00536186.68800.205364.8695821.73954.4643 2138.59100.02590.00505197.84740.195055.126824.11904.70452146.00510.02170.00444225.02560.204444.891322.17424.5334 2245.92330.02180.00423236.43850.194235.148624.57634.77342255.20610.01810.00369271.03070.203694.909422.55464.5941 2354.64870.01830.00354282.36180.193545.166824.97884.83442366.24740.01510.00307326.23690.203074.924522.88674.6475 2465.03200.01540.00297337.01050.192975.182225.33254.88832479.49680.01260.00255392.48420.202554.937123.17604.6943 2577.38810.01290.00249402.04250.192495.195125.64264.93592595.39620.01050.00212471.98110.202124.947623.42764.7352 2692.09180.01090.00209479.43060.192095.206025.91414.977726114.47550.00870.00176567.37730.201764.956323.64604.7709 27109.58930.00910.00175571.52240.191755.215126.15145.014527137.37060.00730.00147681.85280.201474.963623.83534.8020 28130.41120.00770.00147681.11160.191475.222826.35845.046828164.84470.00610.00122819.22330.201224.969723.99914.8291 29155.18930.00640.00123811.52280.191235.229226.53885.075129197.81360.00510.00102984.06800.201024.974724.14064.8527 30184.67530.00540.00103966.71220.191035.2346626.69585.099830237.37630.00420.000851,181.88160.200854.9789424.26284.8731 31219.76360.00460.000871,151.38750.190875.239226.83245.121531284.85160.00350.000701,419.25790.200704.982424.36814.8908 32261.51870.00380.000731,371.15110.190735.243026.95095.140332341.82190.00290.000591,704.10950.200594.985424.45884.9061 33311.20730.00320.000611,632.66980.190615.246227.05375.156833410.18630.00240.000492,045.93140.200494.987824.53684.9194 34370.33660.00270.000511,943.87710.190515.248927.14285.171134492.22350.00200.000412,456.11760.200414.989824.60384.9308 35440.70060.00230.000432,314.21370.190435.251227.22005.183635590.66820.00170.000342,948.34110.200344.991524.66144.9406 36524.43370.00190.000362,754.91430.190365.253127.28675.194436708.80190.00140.000283,539.00940.200284.992924.71084.9491 37624.07610.00160.000303,279.34810.190305.254727.34445.203837850.56220.00120.000244,247.81120.200244.994124.75314.9564 38742.65060.00130.000263,903.42420.190265.256127.39425.2119381,020.67470.00100.000205,098.37350.200204.995124.78944.9627 39883.75420.00110.000224,646.07480.190225.257227.43725.2190391,224.80960.00080.000166,119.04820.200164.995924.82044.9681 401,051.66750.00100.000185,529.82900.190185.258227.47435.2251401,469.77160.00070.000147,343.85780.200144.996624.84694.9728 484,229.160.00020.0000422,253.480.190045.261927.635.2518486,319.750.00020.0000331,593.740.200034.999224.95814.9924 5412,009.800.00010.0000263,204.230.190025.262727.675.25875418,870.670.00010.0000194,348.340.200014.999724.98444.9971 6034,104.970.00000.00001179,494.580.190015.263027.695.26146056,347.510.00000.00000281,732.570.200004.999924.99424.9989 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  22. 22. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 22 21%21.00%22%22.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.21000.82641.000001.00001.210000.82640.00000.000011.22000.81971.000001.00001.220000.81970.00000.0000 21.46410.68300.452492.21000.662491.50950.68300.452521.48840.67190.450452.22000.670451.49150.67190.4505 31.77160.56450.272183.67410.482182.07391.81200.873731.81580.55070.269663.70840.489662.04221.77330.8683 42.14360.46650.183635.44570.393632.54043.21151.264142.21530.45140.181025.52420.401022.49363.12751.2542 52.59370.38550.131777.58920.341772.92604.75371.624652.70270.37000.129217.73960.349212.86364.60751.6090 63.13840.31860.0982010.18300.308203.24466.34681.956163.29730.30330.0957610.44230.315763.16696.12391.9337 73.79750.26330.0750713.32140.285073.50797.92682.259774.02270.24860.0727813.73960.292783.41557.61542.2297 84.59500.21760.0584117.11890.268413.72569.45022.536684.90770.20380.0563017.76230.276303.61939.04172.4982 95.55990.17990.0460521.71390.256053.905410.88912.788295.98740.16700.0441122.67000.264113.786310.37792.7409 106.72750.14860.0366727.27380.246674.0540812.22693.0159107.30460.13690.0348928.65740.254893.9231811.61002.9593 118.14030.12280.0294134.00130.239414.176913.45533.2213118.91170.11220.0278135.96200.247814.035412.73213.1551 129.84970.10150.0237342.14160.233734.278414.57213.40591210.87220.09200.0222844.87370.242284.127413.74383.3299 1311.91820.08390.0192351.99130.229234.362415.57903.57121313.26410.07540.0179455.74590.237944.202814.64853.4855 1414.42100.06930.0156563.90950.225654.431716.48043.71881416.18220.06180.0144969.01000.234494.264615.45193.6233 1517.44940.05730.0127778.33050.222774.489017.28283.85001519.74230.05070.0117485.19220.231744.315216.16103.7451 1621.11380.04740.0104495.77990.220444.536417.99323.96641624.08560.04150.00953104.93450.229534.356716.78383.8524 1725.54770.03910.00855116.89370.218554.575518.61954.06941729.38440.03400.00775129.02010.227754.390817.32833.9465 1830.91270.03230.00702142.44130.217024.607919.16944.16021835.84900.02790.00631158.40450.226314.418717.80254.0289 1937.40430.02670.00577173.35400.215774.634619.65064.24001943.73580.02290.00515194.25350.225154.441518.21414.1009 2045.25930.02210.00474210.75840.214744.6566920.07044.31002053.35760.01870.00420237.98930.224204.4602718.57024.1635 2154.76370.01830.00391256.01760.213914.675020.43564.37132165.09630.01540.00343291.34690.223434.475618.87744.2178 2266.26410.01510.00322310.78130.213224.690020.75264.42482279.41750.01260.00281356.44320.222814.488219.14184.2649 2380.17950.01250.00265377.04540.212654.702521.02694.47142396.88940.01030.00229435.86070.222294.498519.36894.3056 2497.01720.01030.00219457.22490.212194.712821.26404.511924118.20500.00850.00188532.75010.221884.507019.56354.3407 25117.39090.00850.00180554.24220.211804.721321.46854.547125144.21010.00690.00154650.95510.221544.513919.72994.3709 26142.04290.00700.00149671.63300.211494.728421.64454.577626175.93640.00570.00126795.16530.221264.519619.87204.3968 27171.87190.00580.00123813.67590.211234.734221.79574.603927214.64240.00470.00103971.10160.221034.524319.99314.4191 28207.96510.00480.00101985.54790.211014.739021.92564.626628261.86370.00380.000841,185.74400.220844.528120.09624.4381 29251.63770.00400.000841,193.51290.210844.743022.03684.646229319.47370.00310.000691,447.60770.220694.531220.18394.4544 30304.48160.00330.000691,445.15070.210694.7462722.13214.663130389.75790.00260.000571,767.08130.220574.5337920.25834.4683 31368.42280.00270.000571,749.63230.210574.749022.21354.677531475.50460.00210.000462,156.83920.220464.535920.32144.4801 32445.79160.00220.000472,118.05510.210474.751222.28304.690032580.11560.00170.000382,632.34390.220384.537620.37484.4902 33539.40780.00190.000392,563.84670.210394.753122.34244.700633707.74110.00140.000313,212.45950.220314.539020.42004.4988 34652.68340.00150.000323,103.25450.210324.754622.39294.709734863.44410.00120.000263,920.20060.220264.540220.45824.5060 35789.74700.00130.000273,755.93790.210274.755922.43604.7175351,053.40180.00090.000214,783.64470.220214.541120.49054.5122 36955.59380.00100.000224,545.68480.210224.756922.47264.7242361,285.15020.00080.000175,837.04660.220174.541920.51784.5174 371,156.26850.00090.000185,501.27870.210184.757822.50374.7299371,567.88330.00060.000147,122.19680.220144.542620.54074.5218 381,399.08490.00070.000156,657.54720.210154.758522.53024.7347381,912.81760.00050.000128,690.08010.220124.543120.56014.5256 391,692.89270.00060.000128,056.63210.210124.759122.55264.7389392,333.63750.00040.0000910,602.89780.220094.543520.57634.5287 402,048.40020.00050.000109,749.52480.210104.759622.57174.7424402,847.03780.00040.0000812,936.53530.220084.543920.59004.5314 489,412.340.00010.0000244,815.920.210024.761422.654.75684813,972.430.00010.0000263,506.490.220024.545120.64414.5420 5429,539.970.00000.00001140,661.740.210014.761722.674.76015446,071.340.00000.00000209,410.640.220004.545420.65544.5443 6092,709.070.00000.00000441,466.990.210004.761922.674.761360151,911.220.00000.00000690,500.980.220004.545420.65924.5451 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  23. 23. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 23 23%23.00%24%24.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.23000.81301.000001.00001.230000.81300.00000.000011.24000.80651.000001.00001.240000.80650.00000.0000 21.51290.66100.448432.23000.678431.47400.66100.448421.53760.65040.446432.24000.686431.45680.65040.4464 31.86090.53740.267173.74290.497172.01141.73580.863031.90660.52450.264723.77760.504721.98131.69930.8577 42.28890.43690.178455.60380.408452.44833.04641.244342.36420.42300.175935.68420.415932.40432.96831.2346 52.81530.35520.126707.89260.356702.80354.46721.593552.93160.34110.124258.04840.364252.74544.33271.5782 63.46280.28880.0933910.70790.323393.09235.91121.911663.63520.27510.0910710.98010.331073.02055.70811.8898 74.25930.23480.0705714.17080.300573.32707.31982.200174.50770.22180.0684214.61530.308423.24237.03922.1710 85.23890.19090.0542618.43000.284263.51798.65602.460585.58950.17890.0522919.12290.292293.42128.29152.4236 96.44390.15520.0422523.66900.272253.67319.89752.694696.93100.14430.0404724.71250.280473.56559.44582.6492 107.92590.12620.0332130.11280.263213.7992711.03302.9040108.59440.11640.0316031.64340.271603.6818610.49302.8499 119.74890.10260.0262938.03880.256293.901812.05883.09051110.65710.09380.0248540.23790.264853.775711.43133.0276 1211.99120.08340.0209347.78770.250933.985212.97613.25601213.21480.07570.0196550.89500.259653.851412.26373.1843 1314.74910.06780.0167359.77880.246734.053013.78973.40231316.38630.06100.0156064.10970.255603.912412.99603.3218 1418.14140.05510.0134274.52800.243424.108214.50633.53111420.31910.04920.0124280.49610.252423.961613.63583.4420 1522.31400.04480.0107992.66940.240794.153015.13373.64411525.19560.03970.00992100.81510.249924.001314.19153.5467 1627.44620.03640.00870114.98340.238704.189415.68023.74281631.24260.03200.00794126.01080.247944.033314.67163.6376 1733.75880.02960.00702142.42950.237024.219016.15423.82891738.74080.02580.00636157.25340.246364.059115.08463.7162 1841.52330.02410.00568176.18830.235684.243116.56363.90361848.03860.02080.00510195.99420.245104.079915.43853.7840 1951.07370.01960.00459217.71160.234594.262716.91603.96841959.56790.01680.00410244.03280.244104.096715.74063.8423 2062.82060.01590.00372268.78530.233724.2786217.21854.02432073.86410.01350.00329303.60060.243294.1102615.99793.8922 2177.26940.01290.00302331.60590.233024.291617.47734.07252191.59150.01090.00265377.46480.242654.121216.21623.9349 2295.04130.01050.00245408.87530.232454.302117.69834.113922113.57350.00880.00213469.05630.242134.130016.40113.9712 23116.90080.00860.00198503.91660.231984.310617.88654.149423140.83120.00710.00172582.62980.241724.137116.55744.0022 24143.78800.00700.00161620.81740.231614.317618.04644.179724174.63060.00570.00138723.46100.241384.142816.68914.0284 25176.85930.00570.00131764.60540.231314.323218.18214.205725216.54200.00460.00111898.09160.241114.147416.79994.0507 26217.53690.00460.00106941.46470.231064.327818.29704.227826268.51210.00370.000901,114.63360.240904.151116.89304.0695 27267.57040.00370.000861,159.00160.230864.331618.39424.246527332.95500.00300.000721,383.14570.240724.154216.97114.0853 28329.11150.00300.000701,426.57190.230704.334618.47634.262528412.86420.00240.000581,716.10070.240584.156617.03654.0987 29404.80720.00250.000571,755.68350.230574.337118.54544.276029511.95160.00200.000472,128.96480.240474.158517.09124.1099 30497.91290.00200.000462,160.49070.230464.3390918.60374.287530634.81990.00160.000382,640.91640.240384.1601017.13694.1193 31612.43280.00160.000382,658.40360.230384.340718.65264.297131787.17670.00130.000313,275.73630.240314.161417.17504.1272 32753.29240.00130.000313,270.83640.230314.342118.69384.305332976.09910.00100.000254,062.91300.240254.162417.20674.1338 33926.54960.00110.000254,024.12870.230254.343118.72834.3122331,210.36290.00080.000205,039.01220.240204.163217.23324.1394 341,139.65600.00090.000204,950.67830.230204.344018.75734.3180341,500.85000.00070.000166,249.37510.240164.163917.25524.1440 351,401.77690.00070.000166,090.33440.230164.344718.78154.3228351,861.05400.00050.000137,750.22510.240134.164417.27344.1479 361,724.18560.00060.000137,492.11130.230134.345318.80184.3269362,307.70700.00040.000109,611.27910.240104.164917.28864.1511 372,120.74830.00050.000119,216.29690.230114.345818.81884.3304372,861.55670.00030.0000811,918.98610.240084.165217.30124.1537 382,608.52040.00040.0000911,337.04510.230094.346218.83304.3333383,548.33030.00030.0000714,780.54280.240074.165517.31164.1560 393,208.48010.00030.0000713,945.56550.230074.346518.84494.3357394,399.92950.00020.0000518,328.87310.240054.165717.32024.1578 403,946.43050.00030.0000617,154.04560.230064.346718.85474.3377405,455.91260.00020.0000422,728.80260.240044.165917.32744.1593 4820,674.990.00000.0000189,886.920.230014.347618.894.34554830,495.860.00000.00001127,061.920.240014.166517.35404.1651 5471,593.900.00000.00000311,273.480.230004.347818.904.347154110,859.010.00000.00000461,908.380.240004.166617.35894.1662 60247,917.220.00000.000001,077,896.590.230004.347818.904.347660402,996.350.00000.000001,679,147.280.240004.166717.36044.1665 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  24. 24. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 24 25%25.00%26%26.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.25000.80001.000001.00001.250000.80000.00000.000011.26000.79371.000001.00001.260000.79370.00000.0000 21.56250.64000.444442.25000.694441.44000.64000.444421.58760.62990.442482.26000.702481.42350.62990.4425 31.95310.51200.262303.81250.512301.95201.66400.852532.00040.49990.259903.84760.519901.92341.62970.8473 42.44140.40960.173445.76560.423442.36162.89281.224942.52050.39680.171005.84800.431002.32022.81991.2154 53.05180.32770.121858.20700.371852.68934.20351.563153.17580.31490.119508.36840.379502.63514.07951.5481 63.81470.26210.0888211.25880.338822.95145.51421.868364.00150.24990.0866211.54420.346622.88505.32901.8472 74.76840.20970.0663415.07350.316343.16116.77252.142475.04190.19830.0643315.54580.324333.08336.51902.1143 85.96050.16780.0504019.84190.300403.32897.94692.387286.35280.15740.0485720.58760.308573.24077.62092.3516 97.45060.13420.0387625.80230.288763.46319.02072.604898.00450.12490.0371226.94040.297123.36578.62032.5613 109.31320.10740.0300733.25290.280073.570509.98702.79711010.08570.09920.0286234.94490.288623.464819.51272.7455 1111.64150.08590.0234942.56610.273493.656410.84602.96631112.70800.07870.0222145.03060.282213.543510.29962.9066 1214.55190.06870.0184554.20770.268453.725111.60203.11451216.01200.06250.0173257.73860.277323.605910.98663.0468 1318.18990.05500.0145468.75960.264543.780112.26173.24371320.17520.04960.0135673.75060.273563.655511.58143.1682 1422.73740.04400.0115086.94950.261503.824112.83343.35591425.42070.03930.0106593.92580.270653.694912.09283.2729 1528.42170.03520.00912109.68680.259123.859313.32603.45301532.03010.03120.00838119.34650.268383.726112.52993.3628 1635.52710.02810.00724138.10850.257243.887413.74823.53661640.35790.02480.00661151.37660.266613.750912.90153.4396 1744.40890.02250.00576173.63570.255763.909914.10853.60841750.85100.01970.00522191.73450.265223.770513.21623.5051 1855.51120.01800.00459218.04460.254593.927914.41473.66981864.07220.01560.00412242.58550.264123.786113.48153.5608 1969.38890.01440.00366273.55580.253663.942414.67413.72221980.73100.01240.00326306.65770.263263.798513.70453.6079 2086.73620.01150.00292342.94470.252923.9538814.89323.766720101.72110.00980.00258387.38870.262583.8083413.89133.6476 21108.42020.00920.00233429.68090.252333.963115.07773.804521128.16850.00780.00204489.10980.262043.816114.04733.6810 22135.52530.00740.00186538.10110.251863.970515.23263.836522161.49240.00620.00162617.27830.261623.822314.17733.7091 23169.40660.00590.00148673.62640.251483.976415.36253.863423203.48040.00490.00128778.77070.261283.827314.28553.7326 24211.75820.00470.00119843.03290.251193.981115.47113.886124256.38530.00390.00102982.25110.261023.831214.37523.7522 25264.69780.00380.000951,054.79120.250953.984915.56183.905225323.04540.00310.000811,238.63630.260813.834214.44953.7685 26330.87220.00300.000761,319.48900.250763.987915.63733.921226407.03730.00250.000641,561.68180.260643.836714.51093.7821 27413.59030.00240.000611,650.36120.250613.990315.70023.934627512.86700.00190.000511,968.71910.260513.838714.56163.7934 28516.98790.00190.000482,063.95150.250483.992315.75243.945728646.21240.00150.000402,481.58600.260403.840214.60343.8028 29646.23490.00150.000392,580.93940.250393.993815.79573.955129814.22760.00120.000323,127.79840.260323.841414.63773.8105 30807.79360.00120.000313,227.17430.250313.9950515.83163.9628301,025.92670.00100.000253,942.02600.260253.8424014.66603.8169 311,009.74200.00100.000254,034.96780.250253.996015.86143.9693311,292.66770.00080.000204,967.95270.260203.843214.68923.8222 321,262.17740.00080.000205,044.70980.250203.996815.88593.9746321,628.76130.00060.000166,260.62040.260163.843814.70833.8265 331,577.72180.00060.000166,306.88720.250163.997515.90623.9791332,052.23920.00050.000137,889.38170.260133.844314.72383.8301 341,972.15230.00050.000137,884.60910.250133.998015.92293.9828342,585.82150.00040.000109,941.62100.260103.844714.73663.8330 352,465.19030.00040.000109,856.76130.250103.998415.93673.9858353,258.13500.00030.0000812,527.44240.260083.845014.74703.8354 363,081.48790.00030.0000812,321.95160.250083.998715.94813.9883364,105.25010.00020.0000615,785.57740.260063.845214.75563.8374 373,851.85990.00030.0000615,403.43960.250063.999015.95743.9904375,172.61520.00020.0000519,890.82760.260053.845414.76253.8390 384,814.82490.00020.0000519,255.29940.250053.999215.96513.9921386,517.49510.00020.0000425,063.44280.260043.845614.76823.8403 396,018.53110.00020.0000424,070.12430.250043.999315.97143.9935398,212.04380.00010.0000331,580.93790.260033.845714.77283.8414 407,523.16380.00010.0000330,088.65540.250033.999515.97663.99474010,347.17520.00010.0000339,792.98170.260033.845814.77663.8423 4844,841.550.00000.00001179,362.200.250013.999916.003.99894865,733.410.00000.00000252,816.960.260003.846114.78993.8454 54171,056.940.00000.00000684,223.770.250004.000016.003.999754263,032.510.00000.000001,011,659.670.260003.846114.79213.8459 60652,530.450.00000.000002,610,117.790.250004.000016.003.9999601,052,525.700.00000.000004,048,171.900.260003.846214.79273.8461 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  25. 25. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 25 27%27.00%28%28.00% n Cantidad Compuesta F/P Valor presente P/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G n Cantidad Compuesta F/P Valor presenteP/F Factorde amorizacion A/F Cantidad compuesta F/A Recuperacion decapital A/P Valor presenteP/A Gradientede valor presenteP/G Gradientede serieanual A/G 11.27000.78741.000001.00001.270000.78740.00000.000011.28000.78131.000001.00001.280000.78130.00000.0000 21.61290.62000.440532.27000.710531.40740.62000.440521.63840.61040.438602.28000.718601.39160.61040.4386 32.04840.48820.257543.88290.527541.89561.59640.842232.09720.47680.255213.91840.535211.86841.56400.8371 42.60140.38440.168605.93130.438602.28002.74961.206042.68440.37250.166246.01560.446242.24102.68161.1966 53.30380.30270.117208.53270.387202.58273.96031.533453.43600.29100.114948.69990.394942.53203.84581.5189 64.19590.23830.0844811.83660.354482.82105.15191.826364.39800.22740.0824012.13590.362402.75944.98261.8057 75.32880.18770.0623716.03240.332373.00876.27792.086675.62950.17760.0604816.53390.340482.93706.04842.0594 86.76750.14780.0468121.36120.316813.15647.31232.316687.20580.13880.0451222.16340.325123.07587.01992.2823 98.59480.11640.0355528.12870.305553.27288.24312.518799.22340.10840.0340529.36920.314053.18427.88732.4770 1010.91530.09160.0272336.72350.297233.364399.06762.69521011.80590.08470.0259138.59260.305913.268928.64962.6460 1113.86250.07210.0209947.63880.290993.43659.78902.84851115.11160.06620.0198450.39850.299843.33519.31132.7919 1217.60530.05680.0162661.50130.286263.493310.41382.98101219.34280.05170.0152665.51000.295263.38689.88002.9172 1322.35880.04470.0126479.10660.282643.538110.95053.09511324.75880.04040.0117984.85290.291793.427210.36473.0243 1428.39570.03520.00986101.46540.279863.573311.40833.19271431.69130.03160.00912109.61170.289123.458710.77493.1153 1536.06250.02770.00770129.86110.277703.601011.79653.27591540.56480.02470.00708141.30290.287083.483411.12003.1923 1645.79940.02180.00603165.92360.276033.622812.12403.34661651.92300.01930.00550181.86770.285503.502611.40893.2572 1758.16520.01720.00472211.72300.274723.640012.39913.40631766.46140.01500.00428233.79070.284283.517711.64973.3117 1873.86980.01350.00371269.88820.273713.653612.62923.45671885.07060.01180.00333300.25210.283333.529411.84953.3573 1993.81470.01070.00291343.75800.272913.664212.82113.499019108.89040.00920.00260385.32270.282603.538612.01483.3953 20119.14460.00840.00229437.57260.272293.6726212.98063.534420139.37970.00720.00202494.21310.282023.5458012.15113.4269 21151.31370.00660.00180556.71730.271803.679213.11273.564021178.40600.00560.00158633.59270.281583.551412.26323.4531 22192.16830.00520.00141708.03090.271413.684413.22203.588622228.35960.00440.00123811.99870.281233.555812.35523.4747 23244.05380.00410.00111900.19930.271113.688513.31223.609123292.30030.00340.000961,040.35830.280963.559212.43043.4925 24309.94830.00320.000871,144.25310.270873.691813.38643.626024374.14440.00270.000751,332.65860.280753.561912.49193.5071 25393.63440.00250.000691,454.20140.270693.694313.44733.640025478.90490.00210.000591,706.80310.280593.564012.54203.5191 26499.91570.00200.000541,847.83580.270543.696313.49743.651626612.99820.00160.000462,185.70790.280463.565612.58283.5289 27634.89290.00160.000432,347.75150.270433.697913.53833.661127784.63770.00130.000362,798.70610.280363.566912.61603.5370 28806.31400.00120.000342,982.64430.270343.699113.57183.6689281,004.33630.00100.000283,583.34380.280283.567912.64283.5435 291,024.01870.00100.000263,788.95830.270263.700113.59913.6754291,285.55040.00080.000224,587.68010.280223.568712.66463.5489 301,300.50380.00080.000214,812.97710.270213.7008613.62143.6806301,645.50460.00060.000175,873.23060.280173.5692612.68223.5532 311,651.63980.00060.000166,113.48090.270163.701513.63963.6849312,106.24580.00050.000137,518.73510.280133.569712.69653.5567 322,097.58260.00050.000137,765.12070.270133.701913.65443.6884322,695.99470.00040.000109,624.98100.280103.570112.70803.5596 332,663.92990.00040.000109,862.70330.270103.702313.66643.6913333,450.87320.00030.0000812,320.97560.280083.570412.71733.5619 343,383.19100.00030.0000812,526.63320.270083.702613.67613.6937344,417.11770.00020.0000615,771.84880.280063.570612.72473.5637 354,296.65250.00020.0000615,909.82420.270063.702813.68413.6956355,653.91060.00020.0000520,188.96650.280053.570812.73073.5652 365,456.74870.00020.0000520,206.47670.270053.703013.69053.6971367,237.00560.00010.0000425,842.87710.280043.570912.73563.5665 376,930.07090.00010.0000425,663.22540.270043.703213.69573.6984379,263.36710.00010.0000333,079.88260.280033.571012.73953.5674 388,801.19000.00010.0000332,593.29630.270033.703313.69993.69943811,857.10990.00010.0000242,343.24980.280023.571112.74263.5682 3911,177.51130.00010.0000241,394.48630.270023.703413.70333.70023915,177.10070.00010.0000254,200.35970.280023.571212.74513.5689 4014,195.43930.00010.0000252,571.99760.270023.703413.70603.70094019,426.68890.00010.0000169,377.46040.280013.571212.74713.5694 4896,067.970.00000.00000355,803.590.270003.703713.723.703248139,984.050.00000.00000499,939.450.280003.571412.75383.5711 54403,088.990.00000.000001,492,918.470.270003.703713.723.703654615,656.350.00000.000002,198,769.100.280003.571412.75483.5713 601,691,310.160.00000.000006,264,107.990.270003.703713.723.7037602,707,685.250.00000.000009,670,300.890.280003.571412.75503.5714 FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES FACTORESDECALCULOPARAUNATASAEFECTIVADE: PAGOSUNICOSPAGOSdeseriesuniformesGRADIENTES
  26. 26. Ing. José Moron Rossel – Docente Titular “C” - uagrm Página 26

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