What is the present value of a \$500 payment to be received in one year if the discount rate is 5\% per annum?

• A. \$495.00
• B. \$475.00
• C. \$525.00
• D. \$476.19

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 given a specific discount rate. The formula for calculating 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 \$500, the discount rate (r) is 5% or 0.05, and the number of periods (n) is 1 year.
3. Step 3: Substitute the given values into the present value formula. Using MathML, the formula becomes: $\mathrm{PV}=\frac{\mathrm{FV}}{(1+r){\mathrm{n}}^{}}$. Replace FV with 500, r with 0.05, and n with 1.
4. Step 4: Simplify the denominator. Calculate (1 + r)^n, which is (1 + 0.05)^1 = 1.05.
5. Step 5: Divide the future value by the calculated denominator. Perform the operation 500 / 1.05 to find the present value.