Final answer:
The student's question involves calculating net premium policy values for a life insurance policy, distinguishing between different timing of death benefits. Without more context on mortality tables and interest rates, the precise calculations cannot be made. Additionally, the example provided with 50-year-old men illustrates the importance of risk differentiation in determining actuarially fair premiums.
Step-by-step explanation:
The question pertains to life insurance mathematics, specifically the calculation of net premium policy values under different scenarios. First, understand that cash-value (whole) life insurance not only provides a death benefit but also has a cash value which serves as a savings account that the policyholder can use during their lifetime.
Scenario (a)
For the calculation of net premium policy value at time 10 with the death benefit payable at the end of the quarter year of death, we must consider the present value of future death benefits and the present value of future premium payments. However, as the exact calculations depend on the mortality table and interest rates used, a generic formula cannot be provided without more context.
Scenario (b)
For scenario b, where the death benefit is payable 3 months after the death of the policyholder, we would adjust our present value calculations to account for the additional 3-month delay in payment. The principle remains similar, but this would slightly decrease the present value of the death benefits due to a further point of time in the future when the benefit is received.
Insurance Premiums Example
Regarding the example with 50-year-old men with and without a family history of cancer, calculating an actuarially fair premium involves determining the expected value of the death benefit based on the probability of each outcome. For instance:
- For men with a family history of cancer: Probability of dying in the next year is 1/50, so the expected payout per person is $100,000 ÷ 50 = $2,000.
- For men without a family history of cancer: Probability of dying in the next year is 1/200, so the expected payout per person is $100,000 ÷ 200 = $500.
If the insurer charges the actuarially fair premium to the entire group without differentiating between the two groups, adverse selection may occur, where higher-risk individuals are more likely to purchase the insurance, potentially leading to higher than expected payouts and financial losses for the insurer.