Matematicas Financieras. La amortización
Enviado por troy1255 • 27 de Noviembre de 2020 • Apuntes • 907 Palabras (4 Páginas) • 172 Visitas
Licenciatura en administración y gestión empresarial
7° Cuatrimestre
Sabatino
Mercado Garcia Troy Alexander.
______________________________________________________________________________
La amortización
Es un método para liquidar deudas contraídas, ya sea en forma de pagos o bien en un solo pago al vencimiento de la obligación a través del método de amortización, la deuda se va pagando al realizarse cada pago parcial, de tal forma que el monto de cada pago sirve en primer lugar para el pago de los intereses y el sobrante se abona al capital hasta ese periodo
Forma para calcular el importe
[pic 1]
Donde:
C= al importe de la deuda o capital prestado
N= número de periodos
I= tasa de interés
R = cuota
Ejemplo
El señor Fernández debe 10 mil pesos, la cantidad que será pagada en 5 años mediante pagos anuales. Si la tasa de interés es del 4%
A) importe de cada pago
B) hacer tabla de amortización
R= 10,000*.40(1+.40)5/(1+.40)^5-1
R= 10,000*.40(1.40)5/1.40*4
R= 4,000(5.37)/5.6
R=4.913.61
TABLA DE AMORTIZACION DE LA DEUDA
Monto del préstamo $10,000 moneda
Plazo 5 Años
Interés 40% porcentaje anual
Pago Anual $4,913.61
Periodo (n) | Saldo inicial ( c ) | Cuota ( R ) | Interés ( i) | Amortización (R-i) | Saldo Final ( C-R) |
1 | $10.000,00 | $4.913,61 | $4.000,00 | $913,61 | $9.086,39 |
2 | $9.086,39 | $4.913,61 | $3.634,56 | $1.279,05 | $7.807,34 |
3 | $7.807,34 | $4.913,61 | $3.122,94 | $1.790,67 | $6.016,66 |
4 | $6.016,66 | $4.913,61 | $2.406,67 | $2.506,94 | $3.509,75 |
5 | $3.509,75 | $4.913,61 | $1.403,89 | $3.509,72 | $0,00 |
Si se tiene un préstamo de 25.000 pesos a un plazo de 5 meses y una tasa del 60% anual calcular el pago mensual y realizar la tabla de amortización
R= 25,000*.05(1+.05)5/(1+.05)^5-1
R=1250(1.05)5/(1.05)^5-1
R=1250(1.276281563)/(1.276281563)-1
R=1250(1.276281563)/0.2276281563
R=5774.369945
Monto del préstamo 25000 moneda
Plazo 5 Meses
Interés 60% porcentaje anual
Pago Anual $5.774,37
Periodo (n) | Saldo inicial ( c ) | Cuota ( R ) | Interés ( i) | Amortización (R-i) | Saldo Final ( C-R) |
1 | $25.000,00 | $5.774,37 | $1.250,00 | $4.524,37 | $20.475,63 |
2 | $20.475,63 | $5.774,37 | $1.023,78 | $4.750,59 | $15.725,04 |
TAREA
Se tiene una Deuda de $150,000.00, a pagar en 48 meses a una tasa de interés anual del 98%. Calcular el pago mensual y realizar la tabla de amortización.
TABLA DE AMORTIZACION DE LA DEUDA
Monto $150,000.00 Préstamo
Plazo 48 meses
Interés 98% Porcentaje Anual 8% Porcentaje Mensual
Pago Mensual $12,539.60
PERIODO ( n ) | SALDO INICIAL ( C ) | CUOTA ( R ) | INTERÉS ( i ) | AMORTIZACIÓN R - i | SALDO FINAL C - R | |
1 | $150,000.00 | $12,539.60 | $12,250.00 | $289.60 | $149,710.40 | |
2 | $149,710.40 | $12,539.60 | $12,226.35 | $313.25 | $149,397.15 | |
3 | $149,397.15 | $12,539.60 | $12,200.77 | $338.83 | $149,058.32 | |
4 | $149,058.32 | $12,539.60 | $12,173.10 | $366.50 | $148,691.81 | |
5 | $148,691.81 | $12,539.60 | $12,143.16 | $396.44 | $148,295.38 | |
6 | $148,295.38 | $12,539.60 | $12,110.79 | $428.81 | $147,866.57 | |
7 | $147,866.57 | $12,539.60 | $12,075.77 | $463.83 | $147,402.74 | |
8 | $147,402.74 | $12,539.60 | $12,037.89 | $501.71 | $146,901.03 | |
9 | $146,901.03 | $12,539.60 | $11,996.92 | $542.68 | $146,358.35 | |
10 | $146,358.35 | $12,539.60 | $11,952.60 | $587.00 | $145,771.34 | |
11 | $145,771.34 | $12,539.60 | $11,904.66 | $634.94 | $145,136.40 | |
12 | $145,136.40 | $12,539.60 | $11,852.81 | $686.79 | $144,449.61 | |
13 | $144,449.61 | $12,539.60 | $11,796.72 | $742.88 | $143,706.73 | |
14 | $143,706.73 | $12,539.60 | $11,736.05 | $803.55 | $142,903.18 | |
15 | $142,903.18 | $12,539.60 | $11,670.43 | $869.17 | $142,034.01 | |
16 | $142,034.01 | $12,539.60 | $11,599.44 | $940.16 | $141,093.85 | |
17 | $141,093.85 | $12,539.60 | $11,522.66 | $1,016.94 | $140,076.91 | |
18 | $140,076.91 | $12,539.60 | $11,439.61 | $1,099.99 | $138,976.93 | |
19 | $138,976.93 | $12,539.60 | $11,349.78 | $1,189.82 | $137,787.11 | |
20 | $137,787.11 | $12,539.60 | $11,252.61 | $1,286.99 | $136,500.13 | |
21 | $136,500.13 | $12,539.60 | $11,147.51 | $1,392.09 | $135,108.04 | |
22 | $135,108.04 | $12,539.60 | $11,033.82 | $1,505.78 | $133,602.26 | |
23 | $133,602.26 | $12,539.60 | $10,910.85 | $1,628.75 | $131,973.51 | |
24 | $131,973.51 | $12,539.60 | $10,777.84 | $1,761.76 | $130,211.75 | |
25 | $130,211.75 | $12,539.60 | $10,633.96 | $1,905.64 | $128,306.11 | |
26 | $128,306.11 | $12,539.60 | $10,478.33 | $2,061.27 | $126,244.84 | |
27 | $126,244.84 | $12,539.60 | $10,310.00 | $2,229.60 | $124,015.23 | |
28 | $124,015.23 | $12,539.60 | $10,127.91 | $2,411.69 | $121,603.55 | |
29 | $121,603.55 | $12,539.60 | $9,930.96 | $2,608.64 | $118,994.90 | |
30 | $118,994.90 | $12,539.60 | $9,717.92 | $2,821.68 | $116,173.22 | |
31 | $116,173.22 | $12,539.60 | $9,487.48 | $3,052.12 | $113,121.10 | |
32 | $113,121.10 | $12,539.60 | $9,238.22 | $3,301.38 | $109,819.72 | |
33 | $109,819.72 | $12,539.60 | $8,968.61 | $3,570.99 | $106,248.73 | |
34 | $106,248.73 | $12,539.60 | $8,676.98 | $3,862.62 | $102,386.11 | |
35 | $102,386.11 | $12,539.60 | $8,361.53 | $4,178.07 | $98,208.05 | |
36 | $98,208.05 | $12,539.60 | $8,020.32 | $4,519.28 | $93,688.77 | |
37 | $93,688.77 | $12,539.60 | $7,651.25 | $4,888.35 | $88,800.42 | |
38 | $88,800.42 | $12,539.60 | $7,252.03 | $5,287.57 | $83,512.85 | |
39 | $83,512.85 | $12,539.60 | $6,820.22 | $5,719.38 | $77,793.47 | |
40 | $77,793.47 | $12,539.60 | $6,353.13 | $6,186.47 | $71,607.00 | |
41 | $71,607.00 | $12,539.60 | $5,847.91 | $6,691.69 | $64,915.31 | |
42 | $64,915.31 | $12,539.60 | $5,301.42 | $7,238.18 | $57,677.13 | |
43 | $57,677.13 | $12,539.60 | $4,710.30 | $7,829.30 | $49,847.83 | |
44 | $49,847.83 | $12,539.60 | $4,070.91 | $8,468.69 | $41,379.13 | |
45 | $41,379.13 | $12,539.60 | $3,379.30 | $9,160.30 | $32,218.83 | |
46 | $32,218.83 | $12,539.60 | $2,631.20 | $9,908.40 | $22,310.43 | |
47 | $22,310.43 | $12,539.60 | $1,822.02 | $10,717.58 | $11,592.85 | |
48 | $11,592.85 | $12,539.60 | $946.75 | $11,592.85 | $0.00 |
...