Patrick has a contract that will pay him $3,500 in 11 months. If money can earn 15%, what will be the value of that contract three months from now?
A) $2,975
B) $3,077
C) $3,150
D) $3,182
E) $3,355

Question

Quizplus · Accepted Answer

To find the value of the contract three months from now, we need to discount the future value ($3,500) back to the present (which is three months from now, not today), using the given interest rate of 15%. Since the interest rate is annual, we first convert it to a monthly rate by dividing by 12. The monthly interest rate is $15\% / 12 = 1.25\%$. The number of months from three months from now until the contract pays out is 8 months (11 months until payment - 3 months = 8 months until payment from three months from now). We use the formula for the present value of a single future sum: $PV = FV / (1 + r)^n$, where $PV$ is the present value, $FV$ is the future value, $r$ is the monthly interest rate (as a decimal), and $n$ is the number of periods. Plugging in the values, we get: $PV = $3,500 / (1 + 0.0125)^8$. Calculating this gives us a present value of approximately $3,182, making option D the correct answer.

Patrick Has a Contract That Will Pay Him $3,500 in 11