Question

The following question will test your skills of time value of money techniques applied to credit cards. Suppose you owe $10,000 on a credit card. The credit card has an APR1 of 18%. In the following questions we will assume you make NO additional charges on your credit card.

a. If you wish to pay of the balance in 5 years, how much should you pay monthly?

b. If you make the required payments calculated in a., at the end of the first year (just after you have made the 12th monthly payment), how much do you owe on the credit card?

c. If you make the required payments calculated in a., how much interest do you pay over the first year?

d. If you make the required payments calculated in a., how much interest do you pay over the five-years?

Appendix VI - Credit Card Minimum Payments The following text from NerdWallet explains the minimum payment on credit card bills (I have included this for students' information; there is no question asked). 'A minimum payment is exactly what it sounds like: It's the bare minimum you're contractually obligated to pay each billing cycle. If you don't pay at least the minimum by the due date, you could be hit with a late fee and penalty APR, or annual percentage rate. After 30 days without paying at least the minimum, your Did you know? account can be reported delinquent and your credit score could also take a hit. In the 1970s, minimum payments "The minimum is really useful if people are a little short equal to 5% of the outstanding balance were the norm. Since then, of income in a particular month -for example, when issuers have reduced the payments - they're in between jobs or they recently had a large in part because lower minimum expense," says Nessa Feddis, senior vice president for payments created more profitable consumer protection and payments at the industry accounts group American Bankers Association. "But it's not something that should be routine." In part, that's because the minimum is usually so low that it just barely exceeds the interest charges that accrue each month on your balance. When you're just paying the minimum, it could take years - in some cases, decades - to pay off your full balance. Paying only the minimum

Answer 1

Month	Monthly Payment	Principal Paid	Interest Paid	Remaining Balance	Total Interest
1	253.93	103.93	150	9896.07	150
2	253.93	105.49	148.44	9790.57	298.44
3	253.93	107.08	146.86	9683.5	445.3
4	253.93	108.68	145.25	9574.81	590.55
5	253.93	110.31	143.62	9464.5	734.17
6	253.93	111.97	141.97	9352.54	876.14
7	253.93	113.65	140.29	9238.89	1016.43
8	253.93	115.35	138.58	9123.54	1155.01
9	253.93	117.08	136.85	9006.46	1291.87
10	253.93	118.84	135.1	8887.62	1426.96
11	253.93	120.62	133.31	8767	1560.28
12	253.93	122.43	131.51	8644.57	1691.78
13	253.93	124.27	129.67	8520.31	1821.45
14	253.93	126.13	127.8	8394.18	1949.26
15	253.93	128.02	125.91	8266.15	2075.17
16	253.93	129.94	123.99	8136.21	2199.16
17	253.93	131.89	122.04	8004.32	2321.2
18	253.93	133.87	120.06	7870.45	2441.27
19	253.93	135.88	118.06	7734.57	2559.33
20	253.93	137.92	116.02	7596.66	2675.34
21	253.93	139.98	113.95	7456.67	2789.29
22	253.93	142.08	111.85	7314.59	2901.14
23	253.93	144.22	109.72	7170.37	3010.86
24	253.93	146.38	107.56	7024	3118.42
25	253.93	148.57	105.36	6875.42	3223.78
26	253.93	150.8	103.13	6724.62	3326.91
27	253.93	153.06	100.87	6571.55	3427.78
28	253.93	155.36	98.57	6416.19	3526.35
29	253.93	157.69	96.24	6258.5	3622.6
30	253.93	160.06	93.88	6098.44	3716.47
31	253.93	162.46	91.48	5935.99	3807.95
32	253.93	164.89	89.04	5771.09	3896.99
33	253.93	167.37	86.57	5603.72	3983.56
34	253.93	169.88	84.06	5433.85	4067.61
35	253.93	172.43	81.51	5261.42	4149.12
36	253.93	175.01	78.92	5086.41	4228.04
37	253.93	177.64	76.3	4908.77	4304.34
38	253.93	180.3	73.63	4728.47	4377.97
39	253.93	183.01	70.93	4545.46	4448.89
40	253.93	185.75	68.18	4359.71	4517.08
41	253.93	188.54	65.4	4171.17	4582.47
42	253.93	191.37	62.57	3979.8	4645.04
43	253.93	194.24	59.7	3785.56	4704.74
44	253.93	197.15	56.78	3588.41	4761.52
45	253.93	200.11	53.83	3388.3	4815.35
46	253.93	203.11	50.82	3185.19	4866.17
47	253.93	206.16	47.78	2979.04	4913.95
48	253.93	209.25	44.69	2769.79	4958.63
49	253.93	212.39	41.55	2557.4	5000.18
50	253.93	215.57	38.36	2341.83	5038.54
51	253.93	218.81	35.13	2123.02	5073.67
52	253.93	222.09	31.85	1900.93	5105.52
53	253.93	225.42	28.51	1675.51	5134.03
54	253.93	228.8	25.13	1446.71	5159.16
55	253.93	232.23	21.7	1214.48	5180.86
56	253.93	235.72	18.22	978.76	5199.08
57	253.93	239.25	14.68	739.51	5213.76
58	253.93	242.84	11.09	496.67	5224.85
59	253.93	246.48	7.45	250.18	5232.3
60	253.93	250.18	3.75	0	5236.06

a) To figure out how much goes toward interest, you need to follow these steps-

1. Find your interest rate that you pay on your card (18% APR, in this case)
2. Convert that annual rate to a monthly rate by dividing by 12 (because there are 12 months in a year — so the rate is 1.5%  per month)
3. Multiply the monthly rate by your credit card balance (1.5% times 10,000 for the first month)
4. The result is how much you’re spending on interest ($150 in this case for the first month)
5. Since no minimum payment has been mentioned we first have to calculate the total amount( Principle+ Interest) for the 5 year period.

From the table we get the montly payments to be $253.93

b) from the table we get the amount owed on the credit card is $8644.57

c)From the table we have the interest for the first 12 months as- $1691.78

d)from the table we get interest for the 5 years as $5236.06