Phoebe realizes that she has charged too much on her credit card and has racked up $7,000 in debt. If she can pay $200 each month and the card charges 17 percent APR (compounded monthly), how long will it take her to pay off the debt?

Question

Quizplus · Accepted Answer

To calculate the time it will take Phoebe to pay off her credit card debt, we can use the formula for the payment on an installment loan: $PMT = P \frac{r(1+r)^n}{(1+r)^n - 1}$, where PMT is the payment amount per period, P is the principal amount (initial loan balance), r is the monthly interest rate (annual rate divided by 12), and n is the number of payments. Rearranging the formula to solve for n gives a more complex equation, which typically requires a financial calculator or spreadsheet to solve directly. Given the options provided and knowing the formula involves logarithmic functions to solve for n when rearranged, we can't solve it directly in this format without computation. However, the correct answer, based on the calculation using the given APR and monthly payment amount, is 48.68 months, which accounts for the compound interest over time.

Phoebe Realizes That She Has Charged Too Much on Her