Final answer:
A ten-year endowment life policy would be recommended for a client desiring $30,000 in ten years as it matures for the desired amount at the end of the specified period. Actuarially fair premiums for two groups of men based on their family cancer history can be computed, and charging a single premium across the entire group can lead to financial instability due to adverse selection.
Step-by-step explanation:
If a client desires to have $30,000 in ten years, the type of whole life policy I would recommend is A. A ten-year endowment. This policy is designed to pay out the face amount of the policy if the insured person is still living at the end of the endowment period, which in this case would be ten years.
Cash-value (whole) life insurance not only provides a death benefit but also accumulates a cash value that can be used by the policyholder. In the case of a ten-year endowment, the client would receive the $30,000 after the ten-year period if they are still alive, thus meeting their financial goal.
To calculate the actuarially fair premium for two groups of 50-year-old men—those with and without a family history of cancer—we would perform the following calculations:
- For the group with a family history of cancer (20% chance of dying in the next year): The fair premium would be ($100,000 death benefit / 50 chance of death) × 0.20 (percentage of the group).
- For the group without a family history of cancer (80% chance of dying in the next year): The fair premium would be ($100,000 death benefit / 200 chance of death) × 0.80 (percentage of the group).
The actuarially fair premium across the entire group is calculated by combining the expected losses from both groups and dividing by the total number of policyholders.
If an insurance company tries to charge the actuarially fair premium for the entire group rather than for each group separately, they may face adverse selection, where those with a family history of cancer are more likely to purchase the insurance, skewing the risk profile and potentially leading to financial losses for the insurer.