What is the present value of a \$200 payment to be received in three years if the discount rate is 8\% per year, compounded annually?

• A. \$147.20
• B. \$160.00
• C. \$180.00
• D. \$158.73

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the concept of present value (PV). Present value is the current worth of a future sum of money, discounted at a specific interest rate. The formula for PV is: PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate, and n is the number of periods.
2. Step 2: Identify the given values in the problem. Here, the future value (FV) is \$200, the discount rate (r) is 8% or 0.08, and the number of periods (n) is 3 years.
3. Step 3: Substitute the given values into the present value formula. Using MathML, the formula becomes: $\mathrm{PV}=\frac{\mathrm{FV}}{(1+r)n^{}}$
4. Step 4: Perform the calculation step-by-step. First, calculate (1 + r), which is (1 + 0.08) = 1.08. Then raise 1.08 to the power of 3 (n = 3). Finally, divide the future value (\$200) by the result of 1.08^3.
5. Step 5: Interpret the result. The calculated present value represents the amount you would need to invest today at an 8% annual interest rate to receive \$200 in three years. Compare the calculated value to the provided options to determine the correct answer.