Answer: $4,287

## Explanation To calculate the breakeven premium for a two-year term insurance policy, we need to find the premium P such that the present value of premiums equals the present value of expected payouts. **Given:** - Face amount: $2,000,000 - Interest rate: 2% per annum with semiannual compounding - Premiums paid annually at beginning of year - Payouts occur halfway through the year - Mortality rates from the table **Step 1: Calculate effective annual rate** With semiannual compounding at 2% per annum: - Semiannual rate = 2%/2 = 1% - Effective annual rate = (1 + 0.01)^2 - 1 = 0.0201 = 2.01% **Step 2: Calculate discount factors** - For payouts at 0.5 years: DF₁ = 1/(1 + 0.01)^1 = 0.9901 - For payouts at 1.5 years: DF₂ = 1/(1 + 0.01)^3 = 0.9706 - For premiums at beginning of year: DF₀ = 1, DF₁ = 1/(1 + 0.0201) = 0.9803 **Step 3: Calculate expected payouts** - Year 1 payout probability: 0.002092 (from table) - Year 2 payout probability: Probability of surviving year 1 × death probability in year 2 = (1 - 0.002092) × 0.002240 = 0.997908 × 0.002240 = 0.002235 **Step 4: Present value of expected payouts** - Year 1: $2,000,000 × 0.002092 × 0.9901 = $4,142.20 - Year 2: $2,000,000 × 0.002235 × 0.9706 = $4,338.27 - Total PV of payouts = $4,142.20 + $4,338.27 = $8,480.47 **Step 5: Present value of premiums** - Premium P paid at time 0 and time 1 - PV of premiums = P + P × 0.9803 = P × (1 + 0.9803) = P × 1.9803 **Step 6: Solve for breakeven premium** P × 1.9803 = $8,480.47 P = $8,480.47 / 1.9803 = $4,282.86 The closest option is **$4,287**.

Author: LeetQuiz Editorial Team