A loan of $16,525 at 10.8% compounded monthly is to be paid off by equal monthly payments of $650. How long will it take to pay off the loan?

Question

Quizplus · Accepted Answer

To determine the time it will take to pay off the loan, we can use the loan amortization formula, which is a form of the present value of an annuity formula. The formula to calculate the number of payments (n) is:$$ n = \frac{\log(\frac{PMT}{PMT - PV \times r})}{\log(1 + r)} $$where:- PMT = monthly payment amount = $650- PV = present value of the loan = $16,525- r = monthly interest rate (annual rate divided by 12) = 10.8% / 12 = 0.9% = 0.009Plugging the values into the formula:$$ n = \frac{\log(\frac{650}{650 - 16525 \times 0.009})}{\log(1 + 0.009)} $$$$ n \approx 29 $$Therefore, it will take approximately 29 months to pay off the loan, making choice B the correct answer.

A Loan of $16,525 at 10