Tim Dodson has borrowed $8,600 to pay for his new car. The annual interest rate on the loan is 9.4 percent, and the loan needs to be repaid in four payments. What will be his annual payment if he begins his payment beginning now? (Round to the nearest dollar.)

Question

Quizplus · Accepted Answer

The loan is an annuity due since payments start immediately. The formula for the present value of an annuity due is $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)$, where PV is the present value of the loan ($8,600), PMT is the annual payment, r is the annual interest rate (9.4% or 0.094), and n is the number of payments (4). Rearranging the formula to solve for PMT gives $PMT = \frac{PV}{\left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)}$. Substituting the given values and solving for PMT yields an annual payment of approximately $2,448.

Tim Dodson Has Borrowed $8,600 to Pay for His New