Answer: $39,176.

## Explanation To solve this problem, we need to find the present value of $50,000 at the end of Year 10, discounted back to the end of Year 5. **Step 1: Understand the timeline** - Cash flow: $50,000 at Year 10 - We need PV at Year 5 - Discount rate: 5% **Step 2: Calculate the number of periods** From Year 5 to Year 10 is 5 years (10 - 5 = 5 periods) **Step 3: Apply the present value formula** The formula for present value is: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - FV = Future Value = $50,000 - r = discount rate = 5% = 0.05 - n = number of periods = 5 **Step 4: Calculate** \[ PV = \frac{50,000}{(1 + 0.05)^5} \] \[ PV = \frac{50,000}{(1.05)^5} \] \[ PV = \frac{50,000}{1.2762815625} \] \[ PV = 39,176.31 \] **Step 5: Compare with options** The calculated value of $39,176.31 is closest to option C: $39,176. **Why not the other options?** - **Option A ($30,696)**: This would be the present value if we discounted $50,000 for 10 years (50,000/(1.05)^10 = 30,696), not for 5 years. - **Option B ($37,311)**: This is incorrect and doesn't match the calculation. - **Option C ($39,176)**: Correct, matches our calculation. **Key Concept**: This question tests understanding of present value calculations and the ability to discount cash flows to different points in time.

Author: LeetQuiz .