Matemticas Financieras Andrs Mora Universidad EAFIT AMORTIZACIN DE PRESTAMOS Amortizar es pagar o redimir el capital de un prstamo mediante cuotas peridicas. En Colombia existen actualmente dos sistemas bsicos de amortizacin de prestamos: Abonos constantes de capital e intereses sobre saldos Cuotas iguales (uniformes o anualidades) de capital e inters.

AMORTIZACIN MEDIANTE ABONOS CONSTANTES DE CAPITAL En este sistema se divide el capital inicial (monto del prstamo) en el numero cuotas con las que se vaya a cancelar, y el resultado es la parte de cada cuota que se abona al capital del prstamo que en este caso siempre es constante. La parte de intereses de la cuota se calcula multiplicando el saldo adeudado del periodo anterior por la tasa de inters efectiva peridica. EL valor de cada una de las cuotas es la simple suma de el abono a capital y la parte de inters, y el nuevo saldo adeudado se encuentra restndole al saldo del periodo anterior el abono a capital de la cuota respectiva.

ABONOS TRIMESTRALES CONSTANTES DE CAPITAL (INTERESES TRIMESTRALES SOBRE SALDOS)

Valor Prstamo Tasa de inters Plazo n Periodo 0 1 2 3 4

$100,000,000.00 6% Efectivo Trimestral 1 Ao 4 Valor Cuota $0.00 $31,000,000.00 $29,500,000.00 $28,000,000.00 $26,500,000.00 Intereses Abono a Capital Saldo Adeudado $0.00 $0.00 $100,000,000.00 $6,000,000.00 $25,000,000.00 $75,000,000.00 $4,500,000.00 $25,000,000.00 $50,000,000.00 $3,000,000.00 $25,000,000.00 $25,000,000.00 $1,500,000.00 $25,000,000.00 $0.00

1

Matemticas Financieras Andrs Mora Universidad EAFIT ABONOS SEMESTRALES CONSTANTES DE CAPITAL (INTERESES TRIMESTRALES SOBRE SALDOS)

Valor Prstamo Tasa de inters Plazo n # de abonos Periodo 0 1 2 3 4

$100,000,000.00 6% Efectivo Trimestral 1 Ao 4 2 Valor Cuota $0.00 $6,000,000.00 $56,000,000.00 $3,000,000.00 $53,000,000.00 Intereses Abono a Capital Saldo Adeudado $0.00 $0.00 $100,000,000.00 $6,000,000.00 $0.00 $100,000,000.00 $6,000,000.00 $50,000,000.00 $50,000,000.00 $3,000,000.00 $0.00 $50,000,000.00 $3,000,000.00 $50,000,000.00 $0.00

ABONOS MENSUALES IGUALES DE CAPITAL (INTERESES MENSUALES SOBRE SALDOS)Valor Prstamo Tasa de inters Tasa de inters Plazo n Periodo 0 1 2 3 4 5 6 7 8 9 10 11 12 $100,000,000.00 6% Efectivo Trimestral 1.9613% Efectivo Mensual 1 Ao 12 Valor Cuota $0.00 $10,294,615.58 $10,131,175.39 $9,967,735.20 $9,804,295.01 $9,640,854.83 $9,477,414.64 $9,313,974.45 $9,150,534.27 $8,987,094.08 $8,823,653.89 $8,660,213.71 $8,496,773.52 Intereses Abono a Capital Saldo Adeudado $0.00 $0.00 $100,000,000.00 $1,961,282.24 $8,333,333.33 $91,666,666.67 $1,797,842.06 $8,333,333.33 $83,333,333.33 $1,634,401.87 $8,333,333.33 $75,000,000.00 $1,470,961.68 $8,333,333.33 $66,666,666.67 $1,307,521.49 $8,333,333.33 $58,333,333.33 $1,144,081.31 $8,333,333.33 $50,000,000.00 $980,641.12 $8,333,333.33 $41,666,666.67 $817,200.93 $8,333,333.33 $33,333,333.33 $653,760.75 $8,333,333.33 $25,000,000.00 $490,320.56 $8,333,333.33 $16,666,666.67 $326,880.37 $8,333,333.33 $8,333,333.33 $163,440.19 $8,333,333.33 $0.00

2

Matemticas Financieras Andrs Mora Universidad EAFIT AMORTIZACIN MEDIANTE CUOTAS CONSTANTES O ANUALIDADES En este sistema lo primero que se debe calcular es el valor de las anualidades y esto se hace con base en el monto del prstamo(VP), la tasa de inters efectiva peridica y el numero de cuotas con las que se cancelar el prstamo. Luego calculamos la parte de inters de cada cuota, que al igual que en el sistema anterior, multiplicando el saldo adeudado del periodo anterior por la tasa de inters efectiva peridica. Como ya conocemos el valor de la cuota y la parte que de esta es inters, el abono a capital se obtiene como la diferencia de los rubros anteriores, es decir, restndole al valor de la cuota la parte de inters de la misma. Por ultimo, el nuevo saldo adeudado se encuentra restndole al saldo del periodo anterior el abono a capital de la cuota respectiva.

PAGOS O CUOTAS TRIMESTRALES IGUALES (CUOTAS CONSTANTES TRIMESTRALES)

Valor Prstamo Tasa de inters Plazo n Periodo 0 1 2 3 4

$100,000,000.00 6% Efectivo Trimestral 1 Ao 4 Valor Cuota $0.00 $28,859,149.24 $28,859,149.24 $28,859,149.24 $28,859,149.24 Intereses Abono a Capital Saldo Adeudado $0.00 $0.00 $100,000,000.00 $6,000,000.00 $22,859,149.24 $77,140,850.76 $4,628,451.05 $24,230,698.19 $52,910,152.57 $3,174,609.15 $25,684,540.08 $27,225,612.49 $1,633,536.75 $27,225,612.49 $0.00

PAGOS O CUOTAS MENSUALES IGUALES (CUOTAS CONSTANTES MENSUALES)Valor Prstamo Tasa de inters Tasa de inters Plazo n $100,000,000.00 6% Efectivo Trimestral 1.9613% Efectivo Mensual 1 Ao 12

3

Matemticas Financieras Andrs Mora Universidad EAFITPeriodo 0 1 2 3 4 5 6 7 8 9 10 11 12 Valor Cuota $0.00 $9,433,489.49 $9,433,489.49 $9,433,489.49 $9,433,489.49 $9,433,489.49 $9,433,489.49 $9,433,489.49 $9,433,489.49 $9,433,489.49 $9,433,489.49 $9,433,489.49 $9,433,489.49 Intereses Abono a Capital Saldo Adeudado $0.00 $0.00 $100,000,000.00 $1,961,282.24 $7,472,207.25 $92,527,792.75 $1,814,731.17 $7,618,758.32 $84,909,034.44 $1,665,305.81 $7,768,183.67 $77,140,850.76 $1,512,949.81 $7,920,539.68 $69,220,311.08 $1,357,605.67 $8,075,883.82 $61,144,427.26 $1,199,214.79 $8,234,274.69 $52,910,152.57 $1,037,717.43 $8,395,772.06 $44,514,380.51 $873,052.64 $8,560,436.85 $35,953,943.66 $705,158.31 $8,728,331.18 $27,225,612.49 $533,971.10 $8,899,518.38 $18,326,094.10 $359,426.43 $9,074,063.06 $9,252,031.05 $181,458.44 $9,252,031.05 $0.00

PAGOS O CUOTAS MENSUALES IGUALES ANTICIPADAS (CUOTAS CONSTANTES MENSUALES ANTICIPADAS)

Valor Prstamo Tasa de inters Tasa de inters Plazo n Periodo 0 1 2 3 4 5 6 7 8 9 10 11 12

$100,000,000.00 6% Efectivo Trimestral 1.9613% Efectivo Mensual 1 Ao 12 Valor Cuota $9,252,031.05 $9,252,031.05 $9,252,031.05 $9,252,031.05 $9,252,031.05 $9,252,031.05 $9,252,031.05 $9,252,031.05 $9,252,031.05 $9,252,031.05 $9,252,031.05 $9,252,031.05 $0.00 Intereses Abono a Capital Saldo Adeudado $0.00 $9,252,031.05 $ 90,747,968.95 $1,779,823.80 $7,472,207.25 $83,275,761.71 $1,633,272.73 $7,618,758.32 $75,657,003.39 $1,483,847.37 $7,768,183.67 $67,888,819.72 $1,331,491.37 $7,920,539.68 $59,968,280.04 $1,176,147.23 $8,075,883.82 $51,892,396.22 $1,017,756.35 $8,234,274.69 $43,658,121.53 $856,258.98 $8,395,772.06 $35,262,349.46 $691,594.20 $8,560,436.85 $26,701,912.62 $523,699.87 $8,728,331.18 $17,973,581.44 $352,512.66 $8,899,518.38 $9,074,063.06 $177,967.99 $9,074,063.06 $0.00 $0.00 $0.00 $0.00

4

Matemticas Financieras Andrs Mora Universidad EAFIT COMPRA DE UN INMUEBLE CUYO 70% SE FINANCIA A 15 AOS PARA AMORTIZARLO MEDIANTE ABONOS MENSUALES CONSTANTES DE CAPITAL E INTERESES SOBRE SALDOSValor Propiedad $ 80,000,000.00 Valor Prstamo $ 56,000,000.00 Tasa de inters 22% Efectivo Anual Tasa de inters 1.6709% Efectivo Mensual Plazo 15 Aos n 180 Periodo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Valor Cuota $0.00 $1,246,813.09 $1,241,614.74 $1,236,416.40 $1,231,218.06 $1,226,019.71 $1,220,821.37 $1,215,623.02 $1,210,424.68 $1,205,226.33 $1,200,027.99 $1,194,829.64 $1,189,631.30 $1,184,432.96 $1,179,234.61 $1,174,036.27 $1,168,837.92 $1,163,639.58 $1,158,441.23 $1,153,242.89 $1,148,044.55 $1,142,846.20 $1,137,647.86 $1,132,449.51 $1,127,251.17 $1,122,052.82 $1,116,854.48 $1,111,656.14 $1,106,457.79 $1,101,259.45 $1,096,061.10 $1,090,862.76 $1,085,664.41 $1,080,466.07 $1,075,267.73 $1,070,069.38 $1,064,871.04 Intereses Abono a Capital Saldo Adeudado $0.00 $0.00 $ 56,000,000.00 $935,701.98 $311,111.11 $55,688,888.89 $930,503.63 $311,111.11 $55,377,777.78 $925,305.29 $311,111.11 $55,066,666.67 $920,106.94 $311,111.11 $54,755,555.56 $914,908.60 $311,111.11 $54,444,444.44 $909,710.26 $311,111.11 $54,133,333.33 $904,511.91 $311,111.11 $53,822,222.22 $899,313.57 $311,111.11 $53,511,111.11 $894,115.22 $311,111.11 $53,200,000.00 $888,916.88 $311,111.11 $52,888,888.89 $883,718.53 $311,111.11 $52,577,777.78 $878,520.19 $311,111.11 $52,266,666.67 $873,321.85 $311,111.11 $51,955,555.56 $868,123.50 $311,111.11 $51,644,444.44 $862,925.16 $311,111.11 $51,333,333.33 $857,726.81 $311,111.11 $51,022,222.22 $852,528.47 $311,111.11 $50,711,111.11 $847,330.12 $311,111.11 $50,400,000.00 $842,131.78 $311,111.11 $50,088,888.89 $836,933.43 $311,111.11 $49,777,777.78 $831,735.09 $311,111.11 $49,466,666.67 $826,536.75 $311,111.11 $49,155,555.56 $821,338.40 $311,111.11 $48,844,444.44 $816,140.06 $311,111.11 $48,533,333.33 $810,941.71 $311,111.11 $48,222,222.22 $805,743.37 $311,111.11 $47,911,111.11 $800,545.02 $311,111.11 $47,600,000.00 $795,346.68 $311,111.11 $47,288,888.89 $790,148.34 $311,111.11 $46,977,777.78 $784,949.99 $311,111.11 $46,666,666.67 $779,751.65 $311,111.11 $46,355,555.56 $774,553.30 $311,111.11 $46,044,444.44 $769,354.96 $311,111.11 $45,733,333.33 $764,156.61 $311,111.11 $45,422,222.22 $758,958.27 $311,111.11 $45,111,111.11 $753,759.93 $311,111.11 $44,800,000.00

5

Matemticas Financieras Andrs Mora Universidad EAFIT37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 $1,059,672.69 $1,054,474.35 $1,049,276.00 $1,044,077.66 $1,038,879.32 $1,033,680.97 $1,028,482.63 $1,023,284.28 $1,018,085.94 $1,012,887.59 $1,007,689.25 $1,002,490.91 $997,292.56 $992,094.22 $986,895.87 $981,697.53 $976,499.18 $971,300.84 $966,102.49 $960,904.15 $955,705.81 $950,507.46 $945,309.12 $940,110.77 $934,912.43 $929,714.08 $924,515.74 $919,317.40 $914,119.05 $908,920.71 $903,722.36 $898,524.02 $893,325.67 $888,127.33 $882,928.99 $877,730.64 $872,532.30 $867,333.95 $862,135.61 $856,937.26 $851,738.92 $846,540.58 $841,342.23 $836,143.89 $830,945.54 $825,747.20 $820,548.85 $815,350.51 $810,152.17 $804,953.82 $748,561.58 $743,363.24 $738,164.89 $732,966.55 $727,768.20 $722,569.86 $717,371.52 $712,173.17 $706,974.83 $701,776.48 $696,578.14 $691,379.79 $686,181.45 $680,983.11 $675,784.76 $670,586.42 $665,388.07 $660,189.73 $654,991.38 $649,793.04 $644,594.70 $639,396.35 $634,198.01 $628,999.66 $623,801.32 $618,602.97 $613,404.63 $608,206.28 $603,007.94 $597,809.60 $592,611.25 $587,412.91 $582,214.56 $577,016.22 $571,817.87 $566,619.53 $561,421.19 $556,222.84 $551,024.50 $545,826.15 $540,627.81 $535,429.46 $530,231.12 $525,032.78 $519,834.43 $514,636.09 $509,437.74 $504,239.40 $499,041.05 $493,842.71 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $44,488,888.89 $44,177,777.78 $43,866,666.67 $43,555,555.56 $43,244,444.44 $42,933,333.33 $42,622,222.22 $42,311,111.11 $42,000,000.00 $41,688,888.89 $41,377,777.78 $41,066,666.67 $40,755,555.56 $40,444,444.44 $40,133,333.33 $39,822,222.22 $39,511,111.11 $39,200,000.00 $38,888,888.89 $38,577,777.78 $38,266,666.67 $37,955,555.56 $37,644,444.44 $37,333,333.33 $37,022,222.22 $36,711,111.11 $36,400,000.00 $36,088,888.89 $35,777,777.78 $35,466,666.67 $35,155,555.56 $34,844,444.44 $34,533,333.33 $34,222,222.22 $33,911,111.11 $33,600,000.00 $33,288,888.89 $32,977,777.78 $32,666,666.67 $32,355,555.56 $32,044,444.44 $31,733,333.33 $31,422,222.22 $31,111,111.11 $30,800,000.00 $30,488,888.89 $30,177,777.78 $29,866,666.67 $29,555,555.56 $29,244,444.44

6

Matemticas Financieras Andrs Mora Universidad EAFIT87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 $799,755.48 $794,557.13 $789,358.79 $784,160.44 $778,962.10 $773,763.76 $768,565.41 $763,367.07 $758,168.72 $752,970.38 $747,772.03 $742,573.69 $737,375.35 $732,177.00 $726,978.66 $721,780.31 $716,581.97 $711,383.62 $706,185.28 $700,986.93 $695,788.59 $690,590.25 $685,391.90 $680,193.56 $674,995.21 $669,796.87 $664,598.52 $659,400.18 $654,201.84 $649,003.49 $643,805.15 $638,606.80 $633,408.46 $628,210.11 $623,011.77 $617,813.43 $612,615.08 $607,416.74 $602,218.39 $597,020.05 $591,821.70 $586,623.36 $581,425.02 $576,226.67 $571,028.33 $565,829.98 $560,631.64 $555,433.29 $550,234.95 $545,036.61 $488,644.37 $483,446.02 $478,247.68 $473,049.33 $467,850.99 $462,652.64 $457,454.30 $452,255.96 $447,057.61 $441,859.27 $436,660.92 $431,462.58 $426,264.23 $421,065.89 $415,867.55 $410,669.20 $405,470.86 $400,272.51 $395,074.17 $389,875.82 $384,677.48 $379,479.14 $374,280.79 $369,082.45 $363,884.10 $358,685.76 $353,487.41 $348,289.07 $343,090.72 $337,892.38 $332,694.04 $327,495.69 $322,297.35 $317,099.00 $311,900.66 $306,702.31 $301,503.97 $296,305.63 $291,107.28 $285,908.94 $280,710.59 $275,512.25 $270,313.90 $265,115.56 $259,917.22 $254,718.87 $249,520.53 $244,322.18 $239,123.84 $233,925.49 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $28,933,333.33 $28,622,222.22 $28,311,111.11 $28,000,000.00 $27,688,888.89 $27,377,777.78 $27,066,666.67 $26,755,555.56 $26,444,444.44 $26,133,333.33 $25,822,222.22 $25,511,111.11 $25,200,000.00 $24,888,888.89 $24,577,777.78 $24,266,666.67 $23,955,555.56 $23,644,444.44 $23,333,333.33 $23,022,222.22 $22,711,111.11 $22,400,000.00 $22,088,888.89 $21,777,777.78 $21,466,666.67 $21,155,555.56 $20,844,444.44 $20,533,333.33 $20,222,222.22 $19,911,111.11 $19,600,000.00 $19,288,888.89 $18,977,777.78 $18,666,666.67 $18,355,555.56 $18,044,444.44 $17,733,333.33 $17,422,222.22 $17,111,111.11 $16,800,000.00 $16,488,888.89 $16,177,777.78 $15,866,666.67 $15,555,555.56 $15,244,444.44 $14,933,333.33 $14,622,222.22 $14,311,111.11 $14,000,000.00 $13,688,888.89

7

Matemticas Financieras Andrs Mora Universidad EAFIT137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 $539,838.26 $534,639.92 $529,441.57 $524,243.23 $519,044.88 $513,846.54 $508,648.20 $503,449.85 $498,251.51 $493,053.16 $487,854.82 $482,656.47 $477,458.13 $472,259.78 $467,061.44 $461,863.10 $456,664.75 $451,466.41 $446,268.06 $441,069.72 $435,871.37 $430,673.03 $425,474.69 $420,276.34 $415,078.00 $409,879.65 $404,681.31 $399,482.96 $394,284.62 $389,086.28 $383,887.93 $378,689.59 $373,491.24 $368,292.90 $363,094.55 $357,896.21 $352,697.87 $347,499.52 $342,301.18 $337,102.83 $331,904.49 $326,706.14 $321,507.80 $316,309.46 $228,727.15 $223,528.81 $218,330.46 $213,132.12 $207,933.77 $202,735.43 $197,537.08 $192,338.74 $187,140.40 $181,942.05 $176,743.71 $171,545.36 $166,347.02 $161,148.67 $155,950.33 $150,751.99 $145,553.64 $140,355.30 $135,156.95 $129,958.61 $124,760.26 $119,561.92 $114,363.57 $109,165.23 $103,966.89 $98,768.54 $93,570.20 $88,371.85 $83,173.51 $77,975.16 $72,776.82 $67,578.48 $62,380.13 $57,181.79 $51,983.44 $46,785.10 $41,586.75 $36,388.41 $31,190.07 $25,991.72 $20,793.38 $15,595.03 $10,396.69 $5,198.34 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $311,111.11 $13,377,777.78 $13,066,666.67 $12,755,555.56 $12,444,444.44 $12,133,333.33 $11,822,222.22 $11,511,111.11 $11,200,000.00 $10,888,888.89 $10,577,777.78 $10,266,666.67 $9,955,555.56 $9,644,444.44 $9,333,333.33 $9,022,222.22 $8,711,111.11 $8,400,000.00 $8,088,888.89 $7,777,777.78 $7,466,666.67 $7,155,555.56 $6,844,444.44 $6,533,333.33 $6,222,222.22 $5,911,111.11 $5,600,000.00 $5,288,888.89 $4,977,777.78 $4,666,666.67 $4,355,555.56 $4,044,444.44 $3,733,333.33 $3,422,222.22 $3,111,111.11 $2,800,000.00 $2,488,888.89 $2,177,777.78 $1,866,666.67 $1,555,555.56 $1,244,444.44 $933,333.33 $622,222.22 $311,111.11 -$0.00

COMPRA DE UN INMUEBLE CUYO 70% SE FINANCIA A 15 AOS PARA AMORTIZARLO MEDIANTE CUOTAS MENSUALES IGUALES 8

Matemticas Financieras Andrs Mora Universidad EAFIT

Valor Propiedad $ 80,000,000.00 Valor Prstamo $ 56,000,000.00 Tasa de inters 22% Efectivo Anual Tasa de inters 1.6709% Efectivo Mensual Plazo 15 Aos n 180 Periodo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Valor Cuota $0.00 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 Intereses Abono a Capital Saldo Adeudado $0.00 $0.00 $ 56,000,000.00 $935,701.98 $49,924.64 $55,950,075.36 $934,867.79 $50,758.83 $55,899,316.53 $934,019.66 $51,606.96 $55,847,709.57 $933,157.36 $52,469.26 $55,795,240.31 $932,280.65 $53,345.96 $55,741,894.34 $931,389.30 $54,237.32 $55,687,657.02 $930,483.05 $55,143.57 $55,632,513.45 $929,561.66 $56,064.96 $55,576,448.49 $928,624.87 $57,001.75 $55,519,446.74 $927,672.43 $57,954.19 $55,461,492.55 $926,704.08 $58,922.54 $55,402,570.01 $925,719.54 $59,907.08 $55,342,662.93 $924,718.56 $60,908.06 $55,281,754.87 $923,700.84 $61,925.77 $55,219,829.09 $922,666.13 $62,960.49 $55,156,868.60 $921,614.12 $64,012.49 $55,092,856.11 $920,544.54 $65,082.08 $55,027,774.03 $919,457.09 $66,169.53 $54,961,604.50 $918,351.46 $67,275.16 $54,894,329.34 $917,227.37 $68,399.25 $54,825,930.09 $916,084.49 $69,542.13 $54,756,387.95 $914,922.51 $70,704.11 $54,685,683.84 $913,741.12 $71,885.50 $54,613,798.34 $912,539.98 $73,086.64 $54,540,711.70 $911,318.78 $74,307.84 $54,466,403.87 $910,077.17 $75,549.44 $54,390,854.42 $908,814.82 $76,811.80 $54,314,042.62 $907,531.38 $78,095.24 $54,235,947.38 $906,226.49 $79,400.13 $54,156,547.25 $904,899.79 $80,726.83 $54,075,820.42 $903,550.93 $82,075.69 $53,993,744.73 $902,179.53 $83,447.09 $53,910,297.64 $900,785.22 $84,841.40 $53,825,456.23 $899,367.60 $86,259.02 $53,739,197.22 $897,926.30 $87,700.31 $53,651,496.90 $896,460.92 $89,165.70 $53,562,331.21 $894,971.06 $90,655.56 $53,471,675.65 $893,456.30 $92,170.32 $53,379,505.32 $891,916.23 $93,710.39 $53,285,794.93

9

Matemticas Financieras Andrs Mora Universidad EAFIT40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $890,350.42 $888,758.46 $887,139.89 $885,494.28 $883,821.17 $882,120.11 $880,390.62 $878,632.24 $876,844.47 $875,026.83 $873,178.83 $871,299.94 $869,389.66 $867,447.46 $865,472.81 $863,465.16 $861,423.97 $859,348.67 $857,238.70 $855,093.47 $852,912.40 $850,694.88 $848,440.31 $846,148.07 $843,817.53 $841,448.04 $839,038.97 $836,589.64 $834,099.39 $831,567.53 $828,993.36 $826,376.18 $823,715.27 $821,009.90 $818,259.32 $815,462.79 $812,619.53 $809,728.76 $806,789.69 $803,801.51 $800,763.40 $797,674.53 $794,534.04 $791,341.08 $788,094.77 $784,794.22 $781,438.52 $778,026.75 $774,557.97 $771,031.23 $95,276.20 $96,868.16 $98,486.73 $100,132.34 $101,805.45 $103,506.51 $105,236.00 $106,994.38 $108,782.15 $110,599.79 $112,447.79 $114,326.68 $116,236.96 $118,179.16 $120,153.81 $122,161.46 $124,202.65 $126,277.95 $128,387.92 $130,533.15 $132,714.22 $134,931.74 $137,186.31 $139,478.55 $141,809.09 $144,178.57 $146,587.65 $149,036.98 $151,527.23 $154,059.09 $156,633.26 $159,250.44 $161,911.35 $164,616.72 $167,367.30 $170,163.83 $173,007.09 $175,897.86 $178,836.93 $181,825.11 $184,863.22 $187,952.09 $191,092.58 $194,285.54 $197,531.85 $200,832.40 $204,188.10 $207,599.87 $211,068.65 $214,595.39 $53,190,518.73 $53,093,650.57 $52,995,163.84 $52,895,031.50 $52,793,226.05 $52,689,719.54 $52,584,483.54 $52,477,489.15 $52,368,707.00 $52,258,107.22 $52,145,659.42 $52,031,332.74 $51,915,095.78 $51,796,916.62 $51,676,762.81 $51,554,601.36 $51,430,398.71 $51,304,120.76 $51,175,732.84 $51,045,199.70 $50,912,485.47 $50,777,553.73 $50,640,367.43 $50,500,888.88 $50,359,079.79 $50,214,901.21 $50,068,313.56 $49,919,276.58 $49,767,749.35 $49,613,690.26 $49,457,057.00 $49,297,806.56 $49,135,895.21 $48,971,278.49 $48,803,911.19 $48,633,747.36 $48,460,740.27 $48,284,842.41 $48,106,005.47 $47,924,180.36 $47,739,317.14 $47,551,365.05 $47,360,272.47 $47,165,986.93 $46,968,455.08 $46,767,622.68 $46,563,434.58 $46,355,834.71 $46,144,766.06 $45,930,170.67

10

Matemticas Financieras Andrs Mora Universidad EAFIT90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $767,445.56 $763,799.98 $760,093.49 $756,325.06 $752,493.67 $748,598.26 $744,637.77 $740,611.09 $736,517.14 $732,354.77 $728,122.86 $723,820.24 $719,445.73 $714,998.12 $710,476.20 $705,878.72 $701,204.43 $696,452.03 $691,620.22 $686,707.67 $681,713.05 $676,634.97 $671,472.04 $666,222.84 $660,885.93 $655,459.85 $649,943.11 $644,334.19 $638,631.54 $632,833.61 $626,938.81 $620,945.51 $614,852.06 $608,656.80 $602,358.03 $595,954.01 $589,442.98 $582,823.17 $576,092.74 $569,249.85 $562,292.63 $555,219.15 $548,027.49 $540,715.66 $533,281.66 $525,723.45 $518,038.94 $510,226.03 $502,282.58 $494,206.41 $218,181.06 $221,826.64 $225,533.13 $229,301.55 $233,132.95 $237,028.36 $240,988.85 $245,015.53 $249,109.48 $253,271.85 $257,503.76 $261,806.38 $266,180.89 $270,628.50 $275,150.42 $279,747.90 $284,422.19 $289,174.59 $294,006.40 $298,918.94 $303,913.57 $308,991.65 $314,154.58 $319,403.78 $324,740.69 $330,166.77 $335,683.51 $341,292.43 $346,995.08 $352,793.01 $358,687.81 $364,681.11 $370,774.56 $376,969.81 $383,268.59 $389,672.61 $396,183.64 $402,803.45 $409,533.88 $416,376.77 $423,333.99 $430,407.47 $437,599.13 $444,910.96 $452,344.96 $459,903.17 $467,587.68 $475,400.58 $483,344.04 $491,420.21 $45,711,989.61 $45,490,162.97 $45,264,629.84 $45,035,328.29 $44,802,195.34 $44,565,166.99 $44,324,178.13 $44,079,162.60 $43,830,053.12 $43,576,781.27 $43,319,277.52 $43,057,471.14 $42,791,290.25 $42,520,661.76 $42,245,511.34 $41,965,763.44 $41,681,341.25 $41,392,166.65 $41,098,160.25 $40,799,241.30 $40,495,327.73 $40,186,336.08 $39,872,181.50 $39,552,777.72 $39,228,037.04 $38,897,870.27 $38,562,186.76 $38,220,894.33 $37,873,899.25 $37,521,106.24 $37,162,418.43 $36,797,737.32 $36,426,962.77 $36,049,992.95 $35,666,724.36 $35,277,051.75 $34,880,868.11 $34,478,064.66 $34,068,530.78 $33,652,154.01 $33,228,820.01 $32,798,412.55 $32,360,813.42 $31,915,902.46 $31,463,557.50 $31,003,654.33 $30,536,066.65 $30,060,666.07 $29,577,322.03 $29,085,901.82

11

Matemticas Financieras Andrs Mora Universidad EAFIT140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $985,626.62 $485,995.28 $477,646.96 $469,159.15 $460,529.51 $451,755.68 $442,835.25 $433,765.77 $424,544.75 $415,169.65 $405,637.91 $395,946.90 $386,093.96 $376,076.39 $365,891.44 $355,536.30 $345,008.15 $334,304.08 $323,421.15 $312,356.38 $301,106.74 $289,669.12 $278,040.39 $266,217.36 $254,196.77 $241,975.34 $229,549.70 $216,916.43 $204,072.08 $191,013.12 $177,735.95 $164,236.93 $150,512.36 $136,558.47 $122,371.42 $107,947.32 $93,282.21 $78,372.06 $63,212.77 $47,800.19 $32,130.08 $16,198.15 $499,631.34 $507,979.66 $516,467.47 $525,097.11 $533,870.94 $542,791.37 $551,860.85 $561,081.87 $570,456.97 $579,988.71 $589,679.72 $599,532.66 $609,550.23 $619,735.18 $630,090.32 $640,618.47 $651,322.54 $662,205.47 $673,270.24 $684,519.88 $695,957.50 $707,586.23 $719,409.26 $731,429.85 $743,651.28 $756,076.92 $768,710.19 $781,554.54 $794,613.50 $807,890.67 $821,389.69 $835,114.26 $849,068.15 $863,255.20 $877,679.30 $892,344.41 $907,254.56 $922,413.85 $937,826.43 $953,496.53 $969,428.47 $28,586,270.48 $28,078,290.82 $27,561,823.35 $27,036,726.24 $26,502,855.30 $25,960,063.93 $25,408,203.08 $24,847,121.21 $24,276,664.24 $23,696,675.53 $23,106,995.81 $22,507,463.14 $21,897,912.91 $21,278,177.73 $20,648,087.41 $20,007,468.94 $19,356,146.40 $18,693,940.93 $18,020,670.69 $17,336,150.81 $16,640,193.31 $15,932,607.08 $15,213,197.81 $14,481,767.97 $13,738,116.68 $12,982,039.76 $12,213,329.57 $11,431,775.04 $10,637,161.53 $9,829,270.86 $9,007,881.17 $8,172,766.92 $7,323,698.76 $6,460,443.56 $5,582,764.26 $4,690,419.85 $3,783,165.28 $2,860,751.44 $1,922,925.01 $969,428.47 $0.00

12