Question

Assume that you have a balance of $3000 on your MasterCard and that you make no more charges. Assume that MasterCard charges 12% APR and that each month you make only the minimum payment of 5% of the balance.

Find how many months it will take to bring the remaining balance down to $400. (Round your answer to the nearest whole number.)

Please do NOT use Excel

Answer 1

ANSWER: 48 Months

Interest in each month = opening balance * (APR / 12)

We divide by 12 as we are calculating interest for 1 month

= 3000*12/100*1/12=30

Payment in each month = (opening balance + interest for the month) * 5%

closing balance of each month = opening balance + interest - payment

For 1st Month=3000*12/100*1/12=30

=3000+30-5/100

=2878.50

It goes till 48 months to reach the balance down to 400.

48th Month= 429.05*12/100*1/12

=429.05+4.29-21.67

=411.68

Months	Opening Bal	Interest	Total	Mini.Payment	Closing Balance
1	3,000.00	30.00	3,030.00	151.50	2,878.50
2	2,878.50	28.79	2,907.29	145.36	2,761.92
3	2,761.92	27.62	2,789.54	139.48	2,650.06
4	2,650.06	26.50	2,676.56	133.83	2,542.74
5	2,542.74	25.43	2,568.16	128.41	2,439.75
6	2,439.75	24.40	2,464.15	123.21	2,340.94
7	2,340.94	23.41	2,364.35	118.22	2,246.14
8	2,246.14	22.46	2,268.60	113.43	2,155.17
9	2,155.17	21.55	2,176.72	108.84	2,067.88
10	2,067.88	20.68	2,088.56	104.43	1,984.13
11	1,984.13	19.84	2,003.98	100.20	1,903.78
12	1,903.78	19.04	1,922.81	96.14	1,826.67
13	1,826.68	18.27	1,844.94	92.25	1,752.70
14	1,752.70	17.53	1,770.22	88.51	1,681.71
15	1,681.71	16.82	1,698.53	84.93	1,613.60
16	1,613.60	16.14	1,629.74	81.49	1,548.25
17	1,548.25	15.48	1,563.73	78.19	1,485.55
18	1,485.55	14.86	1,500.40	75.02	1,425.38
19	1,425.38	14.25	1,439.64	71.98	1,367.65
20	1,367.66	13.68	1,381.33	69.07	1,312.26
21	1,312.27	13.12	1,325.39	66.27	1,259.12
22	1,259.12	12.59	1,271.71	63.59	1,208.12
23	1,208.12	12.08	1,220.21	61.01	1,159.19
24	1,159.20	11.59	1,170.79	58.54	1,112.25
25	1,112.25	11.12	1,123.37	56.17	1,067.20
26	1,067.20	10.67	1,077.87	53.89	1,023.98
27	1,023.98	10.24	1,034.22	51.71	982.51
28	982.51	9.83	992.33	49.62	942.72
29	942.72	9.43	952.14	47.61	904.54
30	904.54	9.05	913.58	45.68	867.90
31	867.90	8.68	876.58	43.83	832.75
32	832.75	8.33	841.08	42.05	799.03
33	799.03	7.99	807.02	40.35	766.67
34	766.67	7.67	774.33	38.72	735.62
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