Question

2. Ned pays $150 per month on a credit card loan of $10,000, with interest of 24% com- pounded monthly (so 2% per month). Let pn be the amount he owes on the card after n months. (a) Give a recurrence relation for Pn (b) Solve this recurrence relation. (c) After how many months, if ever, will Ned pay off the debt? (d) Changing the payment, what is the maximum payment that Ned can make and never pay off the debt? (What payment keeps the principal constant)?! (e) What should the payment be to pay off the debt within 36 months?

Answer 1

Monthly interest payable on loan amount of $ 10,000/- at 24% is equal to $ 200.

Principal Amount: $ 10,000/-

Interest: 2% per month

Interest Applicable= Compound Interest

Compounding Frequency: Monthly

Annual Percentage Rate (APR): 2% * 12 month =24%

Effective Rate of Interest (EFR) = (1+2%)^12

Therefore EFR =(1+0.02)^12 = 1.2682

To calculate in Percentage =1.2682-1 =0.2682 or 26.82%

1. Please refer to Excel Sheet Calculations, according to which, there is no principal payment by Ned if he pays $ 150 and therefore his liability on credit card loan rises every month.

Monthly Payment	Principal	Principal Payment	Interest Payment	Monthly Payment	Shortfall on Interest Payment
1	10000	0	223.53	150	73.53
2	10073.53	0	225.18	150	75.18
3	10148.71	0	226.86	150	76.86
4	10225.57	0	228.58	150	78.58
5	10304.15	0	230.33	150	80.33
6	10384.48	0	232.13	150	82.13
7	10466.61	0	233.97	150	83.97
8	10550.58	0	235.84	150	85.84
9	10636.42	0	237.76	150	87.76
10	10724.18	0	239.72	150	89.72
11	10813.90	0	241.73	150	91.73
12	10905.63	0	243.78	150	93.78

2. With each passing month, credit card debt for Ned increases if he pays $ 150 per month

C) Payment of $ 150/- per month is grossly inadequate to pay-off the debt of $ 10,000/- as he is paying interest only.

Ned won’t be able to pay his debt if he pay $150 per month.

D) Please refer to excel sheet, according to which Maximum Amount Ned pays $ 223.535 per month to never pay-off the credit card debt.

Monthly Payment	Principal	Principal Payment	Interest Payment	Monthly Payment	Shortfall on Interest Payment
1	10000	0	223.53	223.535	0.00
2	10000.00	0	223.53	223.535	0.00
3	10000.00	0	223.53	223.535	0.00
4	10000.00	0	223.53	223.535	0.00
5	10000.00	0	223.53	223.535	0.00
6	10000.00	0	223.53	223.535	0.00
7	10000.00	0	223.53	223.535	0.00
8	10000.00	0	223.53	223.535	0.00
9	10000.00	0	223.53	223.535	0.00
10	10000.00	0	223.53	223.535	0.00
11	10000.00	0	223.53	223.535	0.00
12	10000.00	0	223.53	223.535	0.00

E) For payment within 36 months, Ned should pay principal

Principal Amount= $ 10,000/-

Tenure: 36 months

Monthly Principal Payable = 10,000/36 = 277.78

Therefore Ned should pay $ 277.78/- principal plus interest as applicable (Please refer to excel sheet for details)