Question

George Costanza has just taken out an $21,581.00, 60-month car loan from his local bank with a 9.00% interest rate compounded monthly. At the end of the second year, George plans on making a $2,757.00 payment directly to the loan’s principal and then to keep on making his regular monthly payments.

What is the balance remaining on the loan after the extra payment to principal is made? (This happens after year 2...)

How many months remain on the loan after the extra payment is made? (Do not round)

Answer 1

Monthly payment is:

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Principle	P	21,581.00
Rate of interest per period:
Annual rate of interest		9.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.09 /12 =	0.7500%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	5
Total number of payments	N	5*12 =	60
Period payment using the formula	=	[ 21581*0.0075*(1+0.0075)^60] / [(1+0.0075 ^60 -1]
Monthly payment	=	447.99

Amortization schedule for the first two years:

Period	Opening liability	Interest expense	EMI Payment	Loan repaid/ (increase)	Closing liability
N	A	B= A* 0.007500	C	D=C-B	E=A-D
1	21,581.00	161.86	447.99	286.13	21,294.87
2	21,294.87	159.71	447.99	288.27	21,006.60
3	21,006.60	157.55	447.99	290.44	20,716.16
4	20,716.16	155.37	447.99	292.61	20,423.55
5	20,423.55	153.18	447.99	294.81	20,128.74
6	20,128.74	150.97	447.99	297.02	19,831.72
7	19,831.72	148.74	447.99	299.25	19,532.47
8	19,532.47	146.49	447.99	301.49	19,230.97
9	19,230.97	144.23	447.99	303.75	18,927.22
10	18,927.22	141.95	447.99	306.03	18,621.19
11	18,621.19	139.66	447.99	308.33	18,312.86
12	18,312.86	137.35	447.99	310.64	18,002.22
13	18,002.22	135.02	447.99	312.97	17,689.25
14	17,689.25	132.67	447.99	315.32	17,373.94
15	17,373.94	130.30	447.99	317.68	17,056.25
16	17,056.25	127.92	447.99	320.06	16,736.19
17	16,736.19	125.52	447.99	322.46	16,413.73
18	16,413.73	123.10	447.99	324.88	16,088.84
19	16,088.84	120.67	447.99	327.32	15,761.52
20	15,761.52	118.21	447.99	329.77	15,431.75
21	15,431.75	115.74	447.99	332.25	15,099.50
22	15,099.50	113.25	447.99	334.74	14,764.76
23	14,764.76	110.74	447.99	337.25	14,427.51
24	14,427.51	108.21	447.99	339.78	14,087.73

Paying 2757 reduces principal balance to 11330.73

Amortization schedule then follows:

Period	Opening liability	Interest expense	EMI Payment	Loan repaid/ (increase)	Closing liability
N	A	B= A* 0.007500	C	D=C-B	E=A-D
25	11,330.73	84.98	447.99	363.01	10,967.72
26	10,967.72	82.26	447.99	365.73	10,602.00
27	10,602.00	79.51	447.99	368.47	10,233.53
28	10,233.53	76.75	447.99	371.23	9,862.29
29	9,862.29	73.97	447.99	374.02	9,488.27
30	9,488.27	71.16	447.99	376.82	9,111.45
31	9,111.45	68.34	447.99	379.65	8,731.80
32	8,731.80	65.49	447.99	382.50	8,349.30
33	8,349.30	62.62	447.99	385.37	7,963.93
34	7,963.93	59.73	447.99	388.26	7,575.68
35	7,575.68	56.82	447.99	391.17	7,184.51
36	7,184.51	53.88	447.99	394.10	6,790.41
37	6,790.41	50.93	447.99	397.06	6,393.35
38	6,393.35	47.95	447.99	400.04	5,993.31
39	5,993.31	44.95	447.99	403.04	5,590.28
40	5,590.28	41.93	447.99	406.06	5,184.22
41	5,184.22	38.88	447.99	409.10	4,775.11
42	4,775.11	35.81	447.99	412.17	4,362.94
43	4,362.94	32.72	447.99	415.26	3,947.68
44	3,947.68	29.61	447.99	418.38	3,529.30
45	3,529.30	26.47	447.99	421.52	3,107.78
46	3,107.78	23.31	447.99	424.68	2,683.10
47	2,683.10	20.12	447.99	427.86	2,255.24
48	2,255.24	16.91	447.99	431.07	1,824.17
49	1,824.17	13.68	447.99	434.30	1,389.86
50	1,389.86	10.42	447.99	437.56	952.30
51	952.30	7.14	447.99	440.84	511.46
52	511.46	3.84	447.99	444.15	67.31
53	67.31	0.50	67.81	67.31	0.00

Total number of months taken to pay balance was 39