Asked by William McGinnis on May 11, 2024
Verified
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
Compounded Monthly
Involves the calculation of interest by applying the interest rate to the sum of the initial principal and any accumulated interest, repeated monthly.
Economic Value
The measurement of the benefit provided by a good or service to an economic agent.
- Establish the forthcoming and existent values of annuities and single lump sums by the application of compound interest.
- Develop skills in financial planning and decision-making based on compound interest calculations.
Verified Answer
MB
Michael BaltasMay 15, 2024
Final Answer :
B
Explanation :
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×1−(1+r)−nrPV = P \times \frac{1 - (1 + r)^{-n}}{r}PV=P×r1−(1+r)−n , 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.
Learning Objectives
- Establish the forthcoming and existent values of annuities and single lump sums by the application of compound interest.
- Develop skills in financial planning and decision-making based on compound interest calculations.
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