Question

A loan will be repaid in 5 years with monthly payments at a nominal interest rate of 9% monthly convertible. The first payment is $1000 and is to be paid one month from the date of the loan. Each succeeding monthly payment will be 2% lower than the prior payment. Calculate the outstanding loan balance immediately after the 40th payment is made.

Answer 1

Calculation of loan amount

Month	Instalment	PV @ 0.75%
1	1000	992.56
2	980.00	965.46
3	960.40	939.11
4	941.19	913.48
5	922.37	888.54
6	903.92	864.29
7	885.84	840.70
8	868.13	817.75
9	850.76	795.43
10	833.75	773.72
11	817.07	752.60
12	800.73	732.06
13	784.72	712.08
14	769.02	692.64
15	753.64	673.74
16	738.57	655.35
17	723.80	637.46
18	709.32	620.06
19	695.14	603.13
20	681.23	586.67
21	667.61	570.66
22	654.26	555.08
23	641.17	539.93
24	628.35	525.19
25	615.78	510.86
26	603.46	496.91
27	591.40	483.35
28	579.57	470.16
29	567.98	457.32
30	556.62	444.84
31	545.48	432.70
32	534.57	420.89
33	523.88	409.40
34	513.41	398.23
35	503.14	387.36
36	493.07	376.78
37	483.21	366.50
38	473.55	356.49
39	464.08	346.76
40	454.80	337.30
41	445.70	328.09
42	436.79	319.14
43	428.05	310.43
44	419.49	301.95
45	411.10	293.71
46	402.88	285.69
47	394.82	277.90
48	386.92	270.31
49	379.19	262.93
50	371.60	255.76
51	364.17	248.77
52	356.89	241.98
53	349.75	235.38
54	342.75	228.95
55	335.90	222.71
56	329.18	216.63
57	322.60	210.71
58	316.14	204.96
59	309.82	199.37
60	303.63	193.93
		29,452.83

Loan amount is 29452.83

Now we will create loan amortization table for 40 Months to calculate closing balance

Month	Opening Balance	Interest	Instalment	Closing Balance
1	29,452.83	220.90	1,000.00	28,673.73
2	28,673.73	215.05	980.00	27,908.78
3	27,908.78	209.32	960.40	27,157.70
4	27,157.70	203.68	941.19	26,420.19
5	26,420.19	198.15	922.37	25,695.97
6	25,695.97	192.72	903.92	24,984.77
7	24,984.77	187.39	885.84	24,286.31
8	24,286.31	182.15	868.13	23,600.34
9	23,600.34	177.00	850.76	22,926.58
10	22,926.58	171.95	833.75	22,264.78
11	22,264.78	166.99	817.07	21,614.69
12	21,614.69	162.11	800.73	20,976.07
13	20,976.07	157.32	784.72	20,348.67
14	20,348.67	152.62	769.02	19,732.27
15	19,732.27	147.99	753.64	19,126.62
16	19,126.62	143.45	738.57	18,531.50
17	18,531.50	138.99	723.80	17,946.68
18	17,946.68	134.60	709.32	17,371.96
19	17,371.96	130.29	695.14	16,807.12
20	16,807.12	126.05	681.23	16,251.94
21	16,251.94	121.89	667.61	15,706.22
22	15,706.22	117.80	654.26	15,169.76
23	15,169.76	113.77	641.17	14,642.36
24	14,642.36	109.82	628.35	14,123.83
25	14,123.83	105.93	615.78	13,613.98
26	13,613.98	102.10	603.46	13,112.62
27	13,112.62	98.34	591.40	12,619.57
28	12,619.57	94.65	579.57	12,134.65
29	12,134.65	91.01	567.98	11,657.68
30	11,657.68	87.43	556.62	11,188.50
31	11,188.50	83.91	545.48	10,726.93
32	10,726.93	80.45	534.57	10,272.81
33	10,272.81	77.05	523.88	9,825.97
34	9,825.97	73.69	513.41	9,386.26
35	9,386.26	70.40	503.14	8,953.52
36	8,953.52	67.15	493.07	8,527.60
37	8,527.60	63.96	483.21	8,108.34
38	8,108.34	60.81	473.55	7,695.60
39	7,695.60	57.72	464.08	7,289.24
40	7,289.24	54.67	454.80	6,889.11

Closing Balance at the end of 40 month = 6889.11