Explanation:
To calculate the breakeven premium for a two-year term insurance policy, we need to find the premium amount that makes the present value of expected premiums equal to the present value of expected payouts.
Given:
$2,000,000Step 1: Calculate effective semiannual rate Since the interest rate is 2% per annum with semiannual compounding:
Step 2: Calculate present value of expected payouts
Year 1 Payout:
$2,000,000 × 0.002092 × 0.990099 = $4,141.67Year 2 Payout:
$2,000,000 × 0.95908 × 0.002240 × 0.970590 = $4,170.67Total PV of expected payouts = $4,141.67 + $4,170.67 = $8,312.34
Step 3: Calculate present value of $1 premium payments
Premium at time 0: $1
Premium at time 1: $1 × (Probability of survival to year 1) × Present value factor
$1 × 0.95908 × 0.980296 = $0.9400Total PV of $1 premium payments = $1 + $0.9400 = $1.9400
Step 4: Calculate breakeven premium
$1 premium payments$8,312.34 ÷ 1.9400 = $4,284.71This value is closest to $4,287 (Option B).
The calculation accounts for:
Ultimate access to all questions.
The relevant interest rate for insurance contracts is 2% per annum (semiannual compounding applies) and all premiums are paid annually at the beginning of the year. A $2,000,000 term insurance contract is being proposed for a 40-year-old male in average health. Assume that payouts occur halfway throughout the year. Using the mortality rates estimated by the U.S. Social Security Administration, which of the following amounts is closest to the insurance company's breakeven premium for a two-year term?
| Age | Probability of Death within 1 Year | Survival Probability | Life Expectancy |
|---|---|---|---|
| 40 | 0.002092 | 0.95908 | 38.53 |
| 41 | 0.002240 | 0.95708 | 37.61 |
A
$4,246
B
$4,287
C
$4,332
D
$8,482
