What is the present value of \$500.00 to be received in two years if the annual interest rate is 5\% compounded annually?

• A. \$476.19
• B. \$500.00
• C. \$450.00
• D. \$453.51

Answer: (D)

Verified step by step guidance

1. Understand the concept of present value: Present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. It is calculated using the formula: PV = FV / (1 + r)^n, where FV is the future value, r is the annual interest rate, and n is the number of years.
2. Identify the given values in the problem: The future value (FV) is \$500.00, the annual interest rate (r) is 5% (or 0.05 in decimal form), and the number of years (n) is 2.
3. Substitute the given values into the formula: PV = 500 / (1 + 0.05)^2. This involves adding 1 to the interest rate (0.05), raising the result to the power of 2, and then dividing the future value (\$500) by this calculated value.
4. Perform the intermediate calculations step-by-step: First, calculate (1 + 0.05) = 1.05. Then, raise 1.05 to the power of 2, which is 1.05^2. Finally, divide \$500 by the result of 1.05^2.
5. Interpret the result: The calculated present value represents the amount you would need to invest today at a 5% annual interest rate to have \$500 in two years. This demonstrates the time value of money concept.