Question

Solve the problem. Use an annual percentage rate table if necessary. Enrique has a 60-month fixed installment loan, with a monthly payment of $77.86. The amount he borrowed was $3,500.00. Instead of making his 12th payment, Enrique is paying the remaining balance on the loan How much interest will Engrique save. Use the actuarial method .

Answer 1

Solution:

Monthly EMI = $77.86

Amount borrowed = $3,500

Let monthly percentage rate = i

Now present value of monthly EMI at i rate will be equal to amount borrowed.

$77.86 * Cumulative PV factor at i rate for 60 periods = $3,500

Cumulative PV factor at i rate for 60 periods = 44.95247

the PV factor falls at discount rate of 1%

Therefore annual percentage rate = 1%

Loan Amortization schedule
Monthly period	EMI	Interest paid	Principal repayment	Loan balance
0				$3,500.00
1	$77.86	$35.00	$42.86	$3,457.14
2	$77.86	$34.57	$43.29	$3,413.85
3	$77.86	$34.14	$43.72	$3,370.13
4	$77.86	$33.70	$44.16	$3,325.97
5	$77.86	$33.26	$44.60	$3,281.37
6	$77.86	$32.81	$45.05	$3,236.32
7	$77.86	$32.36	$45.50	$3,190.83
8	$77.86	$31.91	$45.95	$3,144.88
9	$77.86	$31.45	$46.41	$3,098.46
10	$77.86	$30.98	$46.88	$3,051.59
11	$77.86	$30.52	$47.34	$3,004.25
12	$77.86	$30.04	$47.82	$2,956.43
13	$77.86	$29.56	$48.30	$2,908.13
14	$77.86	$29.08	$48.78	$2,859.35
15	$77.86	$28.59	$49.27	$2,810.09
16	$77.86	$28.10	$49.76	$2,760.33
17	$77.86	$27.60	$50.26	$2,710.07
18	$77.86	$27.10	$50.76	$2,659.31
19	$77.86	$26.59	$51.27	$2,608.05
20	$77.86	$26.08	$51.78	$2,556.27
21	$77.86	$25.56	$52.30	$2,503.97
22	$77.86	$25.04	$52.82	$2,451.15
23	$77.86	$24.51	$53.35	$2,397.80
24	$77.86	$23.98	$53.88	$2,343.92
25	$77.86	$23.44	$54.42	$2,289.50
26	$77.86	$22.89	$54.97	$2,234.53
27	$77.86	$22.35	$55.51	$2,179.02
28	$77.86	$21.79	$56.07	$2,122.95
29	$77.86	$21.23	$56.63	$2,066.32
30	$77.86	$20.66	$57.20	$2,009.12
31	$77.86	$20.09	$57.77	$1,951.35
32	$77.86	$19.51	$58.35	$1,893.00
33	$77.86	$18.93	$58.93	$1,834.07
34	$77.86	$18.34	$59.52	$1,774.56
35	$77.86	$17.75	$60.11	$1,714.44
36	$77.86	$17.14	$60.72	$1,653.72
37	$77.86	$16.54	$61.32	$1,592.40
38	$77.86	$15.92	$61.94	$1,530.47
39	$77.86	$15.30	$62.56	$1,467.91
40	$77.86	$14.68	$63.18	$1,404.73
41	$77.86	$14.05	$63.81	$1,340.92
42	$77.86	$13.41	$64.45	$1,276.47
43	$77.86	$12.76	$65.10	$1,211.37
44	$77.86	$12.11	$65.75	$1,145.62
45	$77.86	$11.46	$66.40	$1,079.22
46	$77.86	$10.79	$67.07	$1,012.15
47	$77.86	$10.12	$67.74	$944.41
48	$77.86	$9.44	$68.42	$876.00
49	$77.86	$8.76	$69.10	$806.90
50	$77.86	$8.07	$69.79	$737.11
51	$77.86	$7.37	$70.49	$666.62
52	$77.86	$6.67	$71.19	$595.43
53	$77.86	$5.95	$71.91	$523.52
54	$77.86	$5.24	$72.62	$450.89
55	$77.86	$4.51	$73.35	$377.54
56	$77.86	$3.78	$74.08	$303.46
57	$77.86	$3.03	$74.83	$228.63
58	$77.86	$2.29	$75.57	$153.06
59	$77.86	$1.53	$76.33	$76.73
60	$77.86	$1.13	$76.73	$0.00

Loan amount balance after 11th payment = $3,004.25

Total amount to be paid at the time of 12th payment to setlle the loan = $3,004.25 + $30.04 = $3,034.29

Total interest saved = Total amount of 60 EMI - Total payment made

= ($77.86 * 60) - ($77.86*11 + $3,034.29) = $780.85