A car loan of $20,000 at a nominal rate r=9% compounded monthly for 48 months requires equal payments at the end each month

Economics Nov 11, 2020

A car loan of $20,000 at a nominal rate r=9% compounded monthly for 48 months requires equal payments at the end each month. What will be the monthly payment A=_ ? What will be the interest payment (In), principal payment (Pn) and remaining balance (Bn) for the first payment (month 1) and the second payment (month 2) respectively? End of Month Interest Payment Repayment of Principal In Pn n Remaining Loan Balance B. $20,000 Bi=? B2=? 0 1,=? 1 2 P1=? P2=? 12=?

Expert Solution

Loan amount (P) = 20,000

Interest rate (r) = 9% compounded monthly which means monthly interest rate is 9% / 12 = 0.0075

Duration of loan (n) = 48 months

EMI = [P * r * (1 + r)^ⁿ] / [(1 + r)^ⁿ - 1]

EMI = [20,000 * 0.0075 * (1 + 0.0075)^⁴⁸] / [(1 + 0.0075)^⁴⁸ - 1] = 497.70

Here is the complete loan sheet:

End of month	Payment made	Interest payment	Repayment of principle	Remaininig loan balance
0				20,000.00
1	497.70	150.00	347.70	19,652.30
2	497.70	147.39	350.31	19,301.99
3	497.70	144.76	352.94	18,949.06
4	497.70	142.12	355.58	18,593.47
5	497.70	139.45	358.25	18,235.22
6	497.70	136.76	360.94	17,874.29
7	497.70	134.06	363.64	17,510.65
8	497.70	131.33	366.37	17,144.28
9	497.70	128.58	369.12	16,775.16
10	497.70	125.81	371.89	16,403.27
11	497.70	123.02	374.68	16,028.59
12	497.70	120.21	377.49	15,651.11
13	497.70	117.38	380.32	15,270.79
14	497.70	114.53	383.17	14,887.62
15	497.70	111.66	386.04	14,501.58
16	497.70	108.76	388.94	14,112.64
17	497.70	105.84	391.86	13,720.79
18	497.70	102.91	394.79	13,325.99
19	497.70	99.94	397.76	12,928.24
20	497.70	96.96	400.74	12,527.50
21	497.70	93.96	403.74	12,123.75
22	497.70	90.93	406.77	11,716.98
23	497.70	87.88	409.82	11,307.16
24	497.70	84.80	412.90	10,894.26
25	497.70	81.71	415.99	10,478.27
26	497.70	78.59	419.11	10,059.16
27	497.70	75.44	422.26	9,636.90
28	497.70	72.28	425.42	9,211.48
29	497.70	69.09	428.61	8,782.86
30	497.70	65.87	431.83	8,351.03
31	497.70	62.63	435.07	7,915.96
32	497.70	59.37	438.33	7,477.63
33	497.70	56.08	441.62	7,036.02
34	497.70	52.77	444.93	6,591.09
35	497.70	49.43	448.27	6,142.82
36	497.70	46.07	451.63	5,691.19
37	497.70	42.68	455.02	5,236.17
38	497.70	39.27	458.43	4,777.74
39	497.70	35.83	461.87	4,315.88
40	497.70	32.37	465.33	3,850.55
41	497.70	28.88	468.82	3,381.73
42	497.70	25.36	472.34	2,909.39
43	497.70	21.82	475.88	2,433.51
44	497.70	18.25	479.45	1,954.06
45	497.70	14.66	483.04	1,471.01
46	497.70	11.03	486.67	984.35
47	497.70	7.38	490.32	494.03
48	497.70	3.70	494.00	0.03

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