What is the present value of a \$750 payment to be received in three years if the discount rate is 5\% per year, compounded annually?

• A. \$712.50
• B. \$675.00
• C. \$750.00
• D. \$647.72

Answer: (D)

Verified step by step guidance

1. Identify the formula for calculating the present value (PV) of a future payment: PV = \( \frac{FV}{(1 + r)^n} \), where FV is the future value, r is the discount rate, and n is the number of periods.
2. Substitute the given values into the formula: FV = 750, r = 0.05 (5% expressed as a decimal), and n = 3 (three years).
3. Simplify the denominator by calculating \( (1 + r)^n \): \( (1 + 0.05)^3 \).
4. Divide the future value (750) by the result of the denominator calculation to find the present value: \( PV = \frac{750}{(1 + 0.05)^3} \).
5. The result of this calculation will give you the present value of the payment, which is the amount you would need to invest today at a 5% annual discount rate to have \$750 in three years.