Question

3. You have a credit card on which you currenty owe $10,000 The card has a 19 99% annual interest rate and requires a minimum monthly payment of $50 Assume that you do not incur any other purchases on the card. (12 points)

a) If you only make the minimum payment, how long will it take you to pay off the card?

b) If you only make the minimum payment, how much total interest will you pay?

c) If you double the minimum payment, how long will t take you to pay off the ca?

d) if you double the minimum payment, how much total interest will you pay?

e) if you pay $400 per month, how long will t take you to pay off the card?

f) If you pay $400 per month, how much total interest will you pay?

g) f you pay $10 per month, how long will t take you to pay off the card7

h) If you pay $10 per month, how much total interest will you pay?

i) Why would a bank want you to make less of a monthly payment?

Answer 1

a) If only minimum payment is made, the card cannot be repaid at all as the annual interest added will be more than the annual payment made. Annual payment = 50 * 12 = $600. Annual interest = 9400 * 20% = $1880.

b) If only the minimum payment is made, the total interest will keep getting computed till eternity.

c) Even double the minimum payment will be annual payment of $1200 against interest of $1760 on closing balance of first year.

d) If even double the minimum payment is made, the total interest will keep getting computed till eternity.

e)

If monthly payment is $ 400, then the workings are as below:

Months	Outstanding	Monthly interest	Payment	Monthly balance outstanding
1	10,000	167	400	9,767
2	9,767	163	400	9,529
3	9,529	159	400	9,288
4	9,288	155	400	9,043
5	9,043	151	400	8,794
6	8,794	147	400	8,540
7	8,540	142	400	8,283
8	8,283	138	400	8,021
9	8,021	134	400	7,754
10	7,754	129	400	7,484
11	7,484	125	400	7,208
12	7,208	120	400	6,929
13	6,929	115	400	6,644
14	6,644	111	400	6,355
15	6,355	106	400	6,061
16	6,061	101	400	5,762
17	5,762	96	400	5,458
18	5,458	91	400	5,149
19	5,149	86	400	4,834
20	4,834	81	400	4,515
21	4,515	75	400	4,190
22	4,190	70	400	3,860
23	3,860	64	400	3,524
24	3,524	59	400	3,183
25	3,183	53	400	2,836
26	2,836	47	400	2,484
27	2,484	41	400	2,125
28	2,125	35	400	1,760
29	1,760	29	400	1,390
30	1,390	23	400	1,013
31	1,013	17	400	630
32	630	10	400	240
33	240	4	244	-

It will take 33 months to pay off the card.

f) Total interest paid is $3044.

g) If one pays $10 per month, it will not be possible to pay off the card.

h) Interest will accrue till eternity.

i) The interest rate on card is 20% which is very high and a source of income for banks. So they will want the payment in the card to be the minimum.