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**

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