Question

Some students have credit cards that carry an interest rate of “APR 24% per year” When the balance on such a card is $5000, the minimum payment is $110.25.

(a) What is the amount of interest in the first payment?

(b) How long will it take, in months, to pay off the balance, if the cardholder continues to make payments of $110.25 per month and adds no other charges to the card?

Answer 1

(a) Monthly (nominal) interest rate = 24%/12 = 2%

Interest in first payment = $5,000 x 2$ = $100

(b) If it takes N months, then

Monthly payment = Loan amount / P/A(2%, N)

$110.25 = $5,000 / P/A(2%, N)

P/A(2%, N) = 45.3515

[1 - (1.02)^-N] / 0.02** = 45.3515

[1 - (1.02)^-N] = 0.9070

(1.02)^-N = 0.0930

(1.02)^N = 1/0.0930 = 10.7561

Taking natural logarithm on both sides.

N x ln 1.02 = ln 10.7561

N x 0.0198 = 2.3755

N = 120 months

**P/A(r%, N) = [1 - (1 + r)^-N] / r