Let's break down and solve the problem step by step using the **Human Life Value (HLV) approach**. ### **Given:** - **Current Age:** 38 years - **Retirement Age:** 67 years - **Years left to work:** 67 - 38 = **29 years** - **Current Annual Salary:** $90,000 - **Annual Salary Increase:** 2% - **Rate of Return (Discount Rate):** 6% - **Tax Bracket:** 25% - **Personal Consumption:** 20% of after-tax income - **Life Insurance Needed:** Present value of future income available to dependents --- ## **Step 1: Calculate After-Tax Income** - After-tax income = Salary × (1 - Tax Rate) - = $90,000 × (1 - 0.25) - = $90,000 × 0.75 - = **$67,500** --- ## **Step 2: Calculate Income Available to Dependents** - 20% of after-tax income is for Larry's personal use, so 80% is for dependents. - Income available for dependents = After-tax income × 0.8 - = $67,500 × 0.8 - = **$54,000** --- ## **Step 3: Find the Present Value of All Future Income to Dependents** This is a **growing annuity** problem: - **PV = Present Value of a growing annuity** - **PV = PMT × [(1 - ((1+g)/(1+r))^n) / (r-g)]** - PMT = First year’s amount to dependents = $54,000 - g = salary growth rate = 2% = 0.02 - r = discount rate = 6% = 0.06 - n = number of years = 29 Plug in the values: ### **Step 3.1: Calculate the factor** - (1 + g) / (1 + r) = (1.02) / (1.06) ≈ 0.962264 - (0.962264)^29 ≈ 0.281 (using calculator) ### **Step 3.2: Plug into the formula** \[ PV = 54,000 \times \frac{1 - 0.281}{0.06 - 0.02} \] \[ PV = 54,000 \times \frac{0.719}{0.04} \] \[ PV = 54,000 \times 17.975 \] \[ PV ≈ 970,650 \] --- ## **Step 4: Match Closest Answer** The closest answer to our calculation is **$925,696**. --- ## **Final Answer:** **Based on the Human Life Value approach to life insurance needs analysis, Larry should purchase $925,696 of life insurance.** --- **Correct Option:** **$925,696**