Explanation:
First, let’s calculate the present value of the expected payout:
If the man dies during the first year, the expected payout is the probability of a 30-year-old dying within one year multiplied by the sum assured:
= 0.001419 × 100,000 = $141.90
Because the payout is made approximately half-way through the year, we discount the expected payout for 6 months:
= 141.90 × 1.02⁻¹ = $139.12
Similarly, if the man dies during the second year, the expected payout is the probability of a 30-year-old surviving for the first year and then dying in the second year multiplied by the sum assured:
[(1 − 0.001419) × 0.001445 × 100,000] × 1.02⁻³ = $135.97
Hence, total expected payout = 139.12 + 135.97 = $275.09
The annual premium P satisfies: P + P × (1 − 0.001419) × 1.02⁻² = 275.09
Solving: P × [1 + 0.998581 × 1.02⁻²] = 275.09 P × [1 + 0.998581 × 0.96117] = 275.09 P × [1 + 0.95981] = 275.09 P × 1.95981 = 275.09 P ≈ 140.37
The break-even premium is closest to $140.37.
Q.1115 The following data gives the mortality experience among males in Europe in 1931.
| Age in years | Probability of death within one year | Survival probability | Life expectancy |
|---|---|---|---|
| 30 | 0.001419 | 0.97372 | 47.52 |
| 31 | 0.001445 | 0.97234 | 46.59 |
| 32 | 0.001478 | 0.97093 | 45.65 |
| 33 | 0.001519 | 0.97093 | 44.73 |
Assuming that:
I. Interest rate = 4%
II. Premiums are paid annually in advance (at the beginning of the year)
III. Compounding is semi-annual
If the policy has a sum assured of $100,000, and a 30-year-old man takes up a term insurance policy that expires in two years, then which of the following is closest to the break-even premium payable by the policyholder?
A
140.37
B
123.62
C
150
D
80
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