# Present Value Calculation for a Future Lump Sum You will receive **$50,000** exactly **5 years** from now. The **discount rate** is **8% per annum, compounded annually**. We need to find the **present value (PV)**. --- ## Step 1: Write the Present Value Formula The formula for the present value of a future sum is: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \( FV \) = Future Value (\$50,000) - \( r \) = Annual discount rate (8% = .08) - \( n \) = Number of periods (5 years) --- ## Step 2: Substitute the Values \[ PV = \frac{50,000}{(1 + .08)^5} \] --- ## Step 3: Calculate the Denominator First, calculate \( 1.08^5 \): \[ 1.08^5 = 1.08 \times 1.08 \times 1.08 \times 1.08 \times 1.08 \] \[ 1.08^2 = 1.1664 \] \[ 1.08^3 = 1.259712 \] \[ 1.08^4 = 1.360489 \] \[ 1.08^5 = 1.469328 \] --- ## Step 4: Compute the Present Value \[ PV = \frac{50,000}{1.469328} \approx 34,027 \] --- ## Step 5: Round to the Nearest Whole Number The present value is **\$34,027** (rounded to the nearest dollar). --- ## Step 6: Select the Answer **Option A. $34,027** --- ## Summary Table | Step | Value | |--------------|------------------| | Future Value | $50,000 | | Years | 5 | | Discount Rate| 8% (.08) | | PV Formula | \( \frac{50,000}{1.469328} \) | | Present Value| $34,027 | --- **Answer: A. $34,027**