Drew receives an inheritance that pays him $50,000 every three months for the next two years.Which of the following is closest to the present value (PV)of this inheritance if the interest rate is 8.5% (EAR)?
A)$354,223
B)$364,309
C)$365,322
D)$400,000
E)$339,782

Question

Quizplus · Accepted Answer

The present value of an annuity is the sum of the present values of each of the individual payments. In this case, we have 8 payments of $50,000 each, occurring every three months for two years. The interest rate is 8.5% EAR, which is equivalent to 2.125% per quarter.The present value of each payment is:PV = $50,000 / (1 + 0.02125)^nwhere n is the number of quarters from now that the payment is received.The present value of all 8 payments is:PV = $50,000 / (1 + 0.02125)^1 + $50,000 / (1 + 0.02125)^2 + ... + $50,000 / (1 + 0.02125)^8= $365,322.26Therefore, the closest answer choice to the present value of this inheritance is C) $365,322.

Drew Receives an Inheritance That Pays Him $50,000 Every Three