Question

Suppose you have accumulated $21,000 in credit card debt. If the interest rate on the credit card is 24.2% APR compounded monthly, how many years will it take you to pay off this debt if you pay $500 per month? (Answer to the nearest tenth of a year)

Answer 1

Credit Card Balance, PV = 21000
APR, i = 24.20% annually or 2.02% Monthly
Monthly Payment, PMT = 500
Number of Payments = n

1st Method ( Using Excel)
Using Excel Formula "=NPER(i,PMT,-PV)"
Using Excel Formula "=NPER(2.02%,500,-21000)"
n = 94.0257 Months
n = 94.0257/12 = 7.8 Years

2nd Method (Using Financial Calculator)
P/Y=12, I/Y=24.20, PV=21000, PMT=-500; CPT,N: N = 94.03 months = 7.8 Years

3rd Method Using Formula
PV = PMT/i *[1 - (1+i)^-n]
21000 = 500/0.0202 *[1 - (1+0.0202)^-n]
21000 = 24793.39 *[1 - (1.0202)^-n]
0.8470 = 1 - (1.0202)^-n
(1.0202)^-n = 1- 0.8470
(1.0202)^-n = 0.1530
Using Natural Log
-n * ln(1.0202) = ln(0.1530)
-n * 0.02= - 1.8773
n = 93.87 Months = 7.8 years