Joey realizes that he has charged too much on his credit card and has racked up $3,000 in debt. If he can pay $150 each month and the card charges 18 percent APR (compounded monthly), how long will it take him to pay off the debt?
A) 13.03 months
B) 14.68 months
C) 20.00 months
D) 23.96 months

Question

Quizplus · Accepted Answer

To calculate the time it will take Joey to pay off his credit card debt, 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 (or initial amount of debt), and n is the number of payments. Rearranging the formula to solve for n gives us $ n = \frac{\log(P) - \log(P - rPV)}{\log(1 + r)} $. Given that the APR is 18%, the monthly interest rate is $ \frac{18\%}{12} = 1.5\% = 0.015 $. Plugging in the values: $ P = 150 $, $ r = 0.015 $, and $ PV = 3000 $, we can solve for n. This calculation shows that it will take Joey approximately 23.96 months to pay off the debt, assuming he makes consistent monthly payments of $150 and the interest is compounded monthly.

Joey Realizes That He Has Charged Too Much on His