Ejercicio Capitalización y amortización. Matemáticas financieras

Grupo Empresarial, PyME dedicada a la importación de refacciones para máquinas de ensamblado de muebles. Solicitó un préstamo bancario hace 11 meses por una cantidad de $5000,000 a 48 meses con una tasa de interés del 14.8% anual fija, considerando una TIIE del mismo porcentaje. El cobro de la comisión por apertura más IVA (1.5%) también se incrementó a la deuda.

1. ¿Cuál será el importe de las mensualidades?

El importe de las mensualidades será de $141,164.25

P=5,000,000

n=48 meses

i=14.8% anual / 12 meses = 1.233% mensual

Comisión = 75,000

MES	CAPITAL	INTERÉS	PAGO	SALDO
1.00	5,087,000.00	62,722.71	141,164.25	5,008,558.46
2.00	5,008,558.46	61,755.53	141,164.25	4,929,149.74
3.00	4,929,149.74	60,776.42	141,164.25	4,848,761.90
4.00	4,848,761.90	59,785.23	141,164.25	4,767,382.89
5.00	4,767,382.89	58,781.83	141,164.25	4,685,000.47
6.00	4,685,000.47	57,766.06	141,164.25	4,601,602.27
7.00	4,601,602.27	56,737.76	141,164.25	4,517,175.78
8.00	4,517,175.78	55,696.78	141,164.25	4,431,708.31
9.00	4,431,708.31	54,642.96	141,164.25	4,345,187.02
10.00	4,345,187.02	53,576.16	141,164.25	4,257,598.93
11.00	4,257,598.93	52,496.19	141,164.25	4,168,930.87
12.00	4,168,930.87	51,402.92	141,164.25	4,079,169.54
13.00	4,079,169.54	50,296.16	141,164.25	3,988,301.45
14.00	3,988,301.45	49,175.76	141,164.25	3,896,312.96
15.00	3,896,312.96	48,041.54	141,164.25	3,803,190.24
16.00	3,803,190.24	46,893.34	141,164.25	3,708,919.33
17.00	3,708,919.33	45,730.98	141,164.25	3,613,486.06
18.00	3,613,486.06	44,554.28	141,164.25	3,516,876.09
19.00	3,516,876.09	43,363.08	141,164.25	3,419,074.92
20.00	3,419,074.92	42,157.19	141,164.25	3,320,067.86
21.00	3,320,067.86	40,936.44	141,164.25	3,219,840.05
22.00	3,219,840.05	39,700.63	141,164.25	3,118,376.43
23.00	3,118,376.43	38,449.58	141,164.25	3,015,661.76
24.00	3,015,661.76	37,183.11	141,164.25	2,911,680.62
25.00	2,911,680.62	35,901.02	141,164.25	2,806,417.39
26.00	2,806,417.39	34,603.13	141,164.25	2,699,856.27
27.00	2,699,856.27	33,289.23	141,164.25	2,591,981.25
28.00	2,591,981.25	31,959.13	141,164.25	2,482,776.12
29.00	2,482,776.12	30,612.63	141,164.25	2,372,224.50
30.00	2,372,224.50	29,249.53	141,164.25	2,260,309.78
31.00	2,260,309.78	27,869.62	141,164.25	2,147,015.15
32.00	2,147,015.15	26,472.70	141,164.25	2,032,323.60
33.00	2,032,323.60	25,058.55	141,164.25	1,916,217.90
34.00	1,916,217.90	23,626.97	141,164.25	1,798,680.62
35.00	1,798,680.62	22,177.73	141,164.25	1,679,694.10
36.00	1,679,694.10	20,710.63	141,164.25	1,559,240.48
37.00	1,559,240.48	19,225.44	141,164.25	1,437,301.66
38.00	1,437,301.66	17,721.93	141,164.25	1,313,859.34
39.00	1,313,859.34	16,199.89	141,164.25	1,188,894.98
40.00	1,188,894.98	14,659.08	141,164.25	1,062,389.80
41.00	1,062,389.80	13,099.27	141,164.25	934,324.82
42.00	934,324.82	11,520.22	141,164.25	804,680.79
43.00	804,680.79	9,921.71	141,164.25	673,438.26
44.00	673,438.26	8,303.49	141,164.25	540,577.50
45.00	540,577.50	6,665.32	141,164.25	406,078.57
46.00	406,078.57	5,006.95	141,164.25	269,921.27
47.00	269,921.27	3,328.13	141,164.25	132,085.15
48.00	132,085.15	1,628.61	133,713.76	-

El día de hoy 27 de febrero el banco le ofrece una mejor tasa y que renueve el crédito, volvería a pagar la comisión por apertura ya que será un crédito diferente. La comisión por apertura más IVA será del 1.8% sobre el total del crédito. La tasa ofrecida es del 13.5% anual fija.

¿Le conviene al Grupo Empresarial renovar el crédito? 

 No le conviene renovar el crédito ya que la cantidad a pagar aumentara por el aumento a la tasa y la comisión por apertura.

MES	CAPITAL	INTERES	PAGO	SALDO
1.00	4,255,978.15	47,879.75	140,872.88	4,162,985.03
2.00	4,162,985.03	46,833.58	140,872.88	4,068,945.73
3.00	4,068,945.73	45,775.64	140,872.88	3,973,848.50
4.00	3,973,848.50	44,705.80	140,872.88	3,877,681.42
5.00	3,877,681.42	43,623.92	140,872.88	3,780,432.46
6.00	3,780,432.46	42,529.87	140,872.88	3,682,089.45
7.00	3,682,089.45	41,423.51	140,872.88	3,582,640.08
8.00	3,582,640.08	40,304.70	140,872.88	3,482,071.90
9.00	3,482,071.90	39,173.31	140,872.88	3,380,372.33
10.00	3,380,372.33	38,029.19	140,872.88	3,277,528.65
11.00	3,277,528.65	36,872.20	140,872.88	3,173,527.97
12.00	3,173,527.97	35,702.19	140,872.88	3,068,357.28
13.00	3,068,357.28	34,519.02	140,872.88	2,962,003.43
14.00	2,962,003.43	33,322.54	140,872.88	2,854,453.09
15.00	2,854,453.09	32,112.60	140,872.88	2,745,692.81
16.00	2,745,692.81	30,889.04	140,872.88	2,635,708.98
17.00	2,635,708.98	29,651.73	140,872.88	2,524,487.83
18.00	2,524,487.83	28,400.49	140,872.88	2,412,015.44
19.00	2,412,015.44	27,135.17	140,872.88	2,298,277.74
20.00	2,298,277.74	25,855.62	140,872.88	2,183,260.49
21.00	2,183,260.49	24,561.68	140,872.88	2,066,949.29
22.00	2,066,949.29	23,253.18	140,872.88	1,949,329.59
23.00	1,949,329.59	21,929.96	140,872.88	1,830,386.68
24.00	1,830,386.68	20,591.85	140,872.88	1,710,105.65
25.00	1,710,105.65	19,238.69	140,872.88	1,588,471.46
26.00	1,588,471.46	17,870.30	140,872.88	1,465,468.89
27.00	1,465,468.89	16,486.53	140,872.88	1,341,082.54
28.00	1,341,082.54	15,087.18	140,872.88	1,215,296.84
29.00	1,215,296.84	13,672.09	140,872.88	1,088,096.05
30.00	1,088,096.05	12,241.08	140,872.88	959,464.26
31.00	959,464.26	10,793.97	140,872.88	829,385.36
32.00	829,385.36	9,330.59	140,872.88	697,843.07
33.00	697,843.07	7,850.73	140,872.88	564,820.92
34.00	564,820.92	6,354.24	140,872.88	430,302.28
35.00	430,302.28	4,840.90	140,872.88	294,270.31
36.00	294,270.31	3,310.54	140,872.88	156,707.97
37.00	156,707.97	1,762.96	158,470.93	0.01

Referencias.

1.    UNADM. (2019). Matemáticas financieras. Unidad 3. Capitalización y amortización.