Sue just purchased an annuity that will pay $24,000 a year for 25 years, starting today. What was the purchase price if the discount rate is 8.5 percent?

Question

Quizplus · Accepted Answer

The annuity pays immediately, making it an annuity due. The formula for the present value of an annuity due is PV = PMT * [(1 - (1 + r)^-n) / r] * (1 + r), where PMT is the annual payment, r is the annual interest rate, and n is the number of periods. Plugging in $24,000 for PMT, 0.085 for r, and 25 for n, and adjusting for the annuity due by multiplying by (1 + r), gives the present value, which matches closest to option E, $266,498.

Sue Just Purchased an Annuity That Will Pay $24,000 a Year