Question

Suppose that you “max out” a credit card to its limit of $14,000 and plan on paying off this $14,000 balance by making minimum payments of $500 (no other charges will be made with this card as you plan on destroying it once the balance is paid off). On the 8th day of each billing cycle, an automatic payment of $500 will be made to the credit card company which processes and records it on the same day as the payment. At the end of each billing cycle the finance charge is added to the account balance to create the beginning balance of the following billing cycle. (APR of 24.10%). Assuming that the average daily balance method is used and that the billing cycle is 30 days in length, determine how long it will take for the credit card to be completely paid off. Include columns showing the beginning balance of each billing cycle, the average daily balance for that cycle, the finance charge, and the ending balance after the finance charge is applied (depending on your set-up you may want to include additional columns). To clarify, the card will be considered to be paid off when the amount owed at the time that the payment is scheduled to be made is $500 or less (essentially meaning that it will be paid off during the first billing cycle that you encounter where the beginning balance is $500 or less).

Answer 1

It will take around 40 months to pay off the outstanding completely. Please see the table below. Please be guided by the second row which explains how each column has been calculated.

Month	Average balance for day 1 to 7	Average balance for day 8 to 30	Average balance for the billing cycle	Finance charges	Opening balance for next billing cycle
	A = E	B = A - 500	C = (7 x A + 23 x B)/30	D = C x APR x 30 / 360	E = B + D
1	14,000.00	13,500.00	13,616.67	273.47	13,773.47
2	13,773.47	13,273.47	13,390.13	268.92	13,542.39
3	13,542.39	13,042.39	13,159.05	264.28	13,306.66
4	13,306.66	12,806.66	12,923.33	259.54	13,066.21
5	13,066.21	12,566.21	12,682.87	254.71	12,820.92
6	12,820.92	12,320.92	12,437.59	249.79	12,570.71
7	12,570.71	12,070.71	12,187.38	244.76	12,315.47
8	12,315.47	11,815.47	11,932.14	239.64	12,055.11
9	12,055.11	11,555.11	11,671.78	234.41	11,789.52
10	11,789.52	11,289.52	11,406.19	229.07	11,518.59
11	11,518.59	11,018.59	11,135.26	223.63	11,242.23
12	11,242.23	10,742.23	10,858.89	218.08	10,960.31
13	10,960.31	10,460.31	10,576.98	212.42	10,672.73
14	10,672.73	10,172.73	10,289.40	206.65	10,379.38
15	10,379.38	9,879.38	9,996.04	200.75	10,080.13
16	10,080.13	9,580.13	9,696.80	194.74	9,774.87
17	9,774.87	9,274.87	9,391.54	188.61	9,463.49
18	9,463.49	8,963.49	9,080.15	182.36	9,145.85
19	9,145.85	8,645.85	8,762.51	175.98	8,821.83
20	8,821.83	8,321.83	8,438.49	169.47	8,491.30
21	8,491.30	7,991.30	8,107.97	162.83	8,154.13
22	8,154.13	7,654.13	7,770.80	156.06	7,810.20
23	7,810.20	7,310.20	7,426.87	149.16	7,459.35
24	7,459.35	6,959.35	7,076.02	142.11	7,101.46
25	7,101.46	6,601.46	6,718.13	134.92	6,736.39
26	6,736.39	6,236.39	6,353.05	127.59	6,363.98
27	6,363.98	5,863.98	5,980.64	120.11	5,984.09
28	5,984.09	5,484.09	5,600.76	112.48	5,596.57
29	5,596.57	5,096.57	5,213.24	104.70	5,201.27
30	5,201.27	4,701.27	4,817.94	96.76	4,798.03
31	4,798.03	4,298.03	4,414.70	88.66	4,386.69
32	4,386.69	3,886.69	4,003.36	80.40	3,967.09
33	3,967.09	3,467.09	3,583.76	71.97	3,539.07
34	3,539.07	3,039.07	3,155.73	63.38	3,102.44
35	3,102.44	2,602.44	2,719.11	54.61	2,657.05
36	2,657.05	2,157.05	2,273.72	45.66	2,202.72
37	2,202.72	1,702.72	1,819.38	36.54	1,739.26
38	1,739.26	1,239.26	1,355.92	27.23	1,266.49
39	1,266.49	766.49	883.15	17.74	784.22
40	784.22	284.22	400.89	8.05	292.28