Let's break down the problem step by step: --- ## Step 1: Understand the Problem **Question:** You would like to have enough money saved to receive $80,000 per year in perpetuity after retirement. You will not work then. How much would you need to have saved in your retirement fund to achieve this goal? *(Assume that the principal is preserved, and you can draw this out in retirement. The annual interest rate is 8 percent.)* --- ## Step 2: Identify the Formula Since you want to **withdraw $80,000 per year forever (perpetuity)** and keep the principal intact, you use the **perpetuity formula**: \[ \text{Present Value} = \frac{\text{Annual Payment}}{\text{Interest Rate}} \] --- ## Step 3: Plug in the Values - Annual Payment = $80,000 - Interest Rate = 8% = .08 \[ \text{Present Value} = \frac{80,000}{.08} \] --- ## Step 4: Calculate \[ \text{Present Value} = \frac{80,000}{.08} = 1,000,000 \] --- ## Step 5: Choose the Correct Answer The options are: - $716,000 - $750,000 - $1,000,000 - $800,000 **Correct answer: $1,000,000** --- ## **Final Answer** **You would need to have $1,000,000 saved in your retirement fund to withdraw $80,000 per year forever at an 8% interest rate.** --- **Summary Table:** | Annual Payment | Interest Rate | Amount Needed | |:--------------:|:------------:|:-------------:| | $80,000 | 8% | $1,000,000 |