Joey realizes that he has charged too much on his credit card and has racked up $4,000 in debt. If he can pay $200 each month and the card charges 20 percent APR (compounded monthly), how long will it take him to pay off the debt?
A) 17.40 months
B) 20.00 months
C) 24.04 months
D) 24.53 months

Question

Quizplus · Accepted Answer

To solve this, we use the formula for the payment on an installment loan: $ P = \frac{rPV}{1 - (1 + r)^{-n}} $, where P is the payment, r is the monthly interest rate, PV is the present value of the loan (initial amount of debt), and n is the number of payments. Rearranging to solve for n gives us $ n = \frac{\log(P) - \log(P - rPV)}{\log(1 + r)} $. Given that the APR is 20%, the monthly interest rate r is $ \frac{20\%}{12} = \frac{0.20}{12} = 0.01667 $. Plugging in the values: $ P = 200 $, $ PV = 4000 $, and $ r = 0.01667 $, we solve for n. This calculation yields a value of approximately 24.53 months, indicating it will take Joey about 24.53 months to pay off the debt if he pays $200 each month at an APR of 20% compounded monthly.

Joey Realizes That He Has Charged Too Much on His