A University of Iowa basketball standout is offered a choice of contracts by the New York Liberty. The first one gives her $100,000 one year from today and $100,000 two years from today. The second one gives her $132,000 one year from today and $66,000 two years from today. As her agent, you must compute the present value of each contract. Which of the following interest rates is the lowest one at which the present value of the second contract exceeds that of the first?
A)7 percent
B)8 percent
C)9 percent
D)10 percent

Question

Quizplus · Accepted Answer

The present value of the first contract is $100,000/(1+r) + $100,000/(1+r)^2. The present value of the second contract is $132,000/(1+r) + $66,000/(1+r)^2. The second contract will have a higher present value if $132,000/(1+r) + $66,000/(1+r)^2 > $100,000/(1+r) + $100,000/(1+r)^2. This inequality simplifies to $32,000/(1+r)^2 > 0, which is true for all positive values of r. Therefore, the lowest interest rate at which the present value of the second contract exceeds that of the first is 0%.

A University of Iowa Basketball Standout Is Offered a Choice