Let's break down the problem step by step: --- ## **Problem Restatement** After retirement, you expect to live for 25 years. You would like to have $70,000 income each year. How much should you have saved in your retirement account to achieve this income, if the annual interest rate is 6%? (Assume you’ll withdraw the payments at the start of every year after retirement.) --- ## **Step 1: Identify the Type of Problem** This is a **present value of an annuity due** problem because: - You want a fixed income for a number of years - Withdrawals are at the **start** of each year (annuity due) --- ## **Step 2: Write Down the Formula** The present value of an annuity due is: \[ PV_{due} = PMT \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right] \times (1 + r) \] Where: - \( PMT = \$70,000 \) - \( r = .06 \) - \( n = 25 \) --- ## **Step 3: Plug in the Numbers** First, calculate the standard present value of an ordinary annuity: \[ PV_{ordinary} = 70,000 \times \left[ \frac{1 - (1 + .06)^{-25}}{.06} \right] \] Calculate \( (1 + .06)^{-25} \): \[ (1.06)^{-25} \approx .233 \] \[ 1 - .233 = .767 \] \[ .767 / .06 = 12.7833 \] \[ PV_{ordinary} = 70,000 \times 12.7833 = 894,831 \] Now, since it's an **annuity due**, multiply by \( (1 + r) \): \[ PV_{due} = 894,831 \times 1.06 = 948,521 \] --- ## **Step 4: Choose the Closest Answer** Looking at the options: - **$948,521.00** is the answer. --- ## **Step 5: Final Answer** ### **You should have about $948,521 saved in your retirement account.** --- ### **Summary Table** | Step | Calculation | |-----------------|-------------| | PV Ordinary | \( 70,000 \times 12.7833 = 894,831 \) | | PV Annuity Due | \( 894,831 \times 1.06 = 948,521 \) | --- Let me know if you need any step explained further!