Jane won a prize: the right to receive 36 payments of $100 per month with the first payment one month from today. If money is worth 6% compounded monthly, what is the economic value of these payments three years from today?
A) $3,287.10
B) $3,933.61
C) $3,489.84
D) $3,600.00
E) $2,256.29

Question

Quizplus · Accepted Answer

The economic value of these payments three years from today can be calculated using the formula for the present value of an annuity. Since Jane will have received 36 payments of $100 each, but we're looking for the value three years (or 36 - 12 = 24 payments) from today, we use the formula for the present value of an annuity: $PV = P \times \frac{1 - (1 + r)^{-n}}{r}$, where P is the payment amount, r is the monthly interest rate, and n is the number of payments remaining. Here, P = $100, r = 0.06/12 = 0.005 (since 6% annual interest compounded monthly gives a monthly rate of 0.5%), and n = 24 (since we're calculating the value 3 years from today, and payments are monthly, 36 - 12 = 24 payments remain). Plugging these values into the formula gives the present value of these remaining payments, which is approximately $3,933.61.

Jane Won a Prize: the Right to Receive 36 Payments