Let's break down the problem: **Given:** - Retirement in 17 years, at age 67 - Lifetime: To age 95 (28 years in retirement) - Current income: $110,000/year (adjusted for inflation) - Needs to replace 85% of income (excluding Social Security) - Social Security: $22,000/year (in today's dollars) - Investment return: 9%/year - Inflation: 3%/year --- ### Step 1: Calculate Required Income at Retirement 85% of $110,000 = **$93,500** Subtract Social Security: $93,500 - $22,000 = **$71,500** (in today's dollars) But, due to inflation, her first year of retirement needs will be higher: Future Value in 17 years = $71,500 × (1.03)^17 = $71,500 × 1.689 ≈ **$120,784** (required in first year of retirement) --- ### Step 2: Calculate the Present Value Needed at Retirement She will withdraw this inflation-adjusted amount for 28 years. The withdrawals will also increase with inflation (3%). The portfolio will earn a return of 9%. This is a growing annuity problem: **Present Value of Growing Annuity Formula:** \[ PV = PMT \times \frac{1 - \left(\frac{1+g}{1+r}\right)^n}{r-g} \] Where: - PMT = $120,784 (first year withdrawal) - r = 9% (investment return) - g = 3% (inflation/growth rate) - n = 28 years Plug in the numbers: \[ PV = 120,784 \times \frac{1 - \left(\frac{1.03}{1.09}\right)^{28}}{0.09-0.03} \] Calculate \((1.03/1.09)^{28}\): \[ 1.03/1.09 = 0.9450 \] \[ 0.9450^{28} \approx 0.205 \] Now, plug in: \[ PV = 120,784 \times \frac{1 - 0.205}{0.06} \] \[ PV = 120,784 \times \frac{0.795}{0.06} \] \[ PV = 120,784 \times 13.25 \] \[ PV \approx 1,600,388 \] --- ### Step 3: Choose the Closest Answer Among the options: - $1,707,090 - $910,250 - $1,613,125 - $2,012,458 The closest answer is **$1,613,125**. --- **Final Answer:** **$1,613,125**