Explanation:
Step 1: 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
Since 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
If the man dies during the second year, the expected payout is the probability of surviving 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
Total expected payout = 139.12 + 135.97 = $275.09
Step 2: Calculate the present value of premiums.
If P is the annual premium, the first premium is received at time zero with a probability of 1. The second premium is received at the beginning of the second year, subject to the probability that the man does not die in the first year, and discounted for 12 months:
Present value of premiums = P + [(1 − 0.001419) × P] / 1.02² = 1.9598P
Step 3: Equate the present values to find P.
275.09 = 1.9598P
P = $140.37
This is the break-even premium.
Q-1: Given the following assumptions: I. Payout is made approximately half-way through the year of death 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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