Final answer:
The policy owner can usually change the death benefit amount in a cash-value life insurance policy. An actuarially fair premium would be $2,000 for those with a family history of cancer and $500 for those without. Charging one premium for all may lead to unprofitable adverse selection.
Step-by-step explanation:
Regarding the question if the policy owner can change the death benefit amount, the answer is true. With cash-value or whole life insurance policies, the policy owner generally has some flexibility to adjust the death benefit. However, this may depend on specific policy terms and could require additional underwriting.
When discussing cash-value life insurance, it's important to understand that this type of policy not only provides a death benefit to beneficiaries upon the policyholder's death but also accumulates cash value over time from a portion of the premiums paid.
This cash value can often be borrowed against or used to pay premiums, and in some cases, may influence the death benefit amount.
Now, turning to the example provided about 50-year-old men and life insurance, let's break down the actuarially fair premium for each group:
- 20% of 1,000 men have a family history of cancer, meaning 200 men would fall into this category. With a 1 in 50 chance of death in the next year, the expected death rate would be 200/50 = 4 men. At $100,000 per death, the total payout expected would be $400,000 for this group.
- 80% without a family history represent 800 men. With a 1 in 200 chance of death, expected deaths would be 800/200 = 4 men. The total payout would similarly be $400,000 for this group.
The actuarially fair premium for the first group with a family history would thus be $400,000 / 200 = $2,000 per person. For the second group, it would also be $400,000 / 800 = $500 per person.
If the insurance company sets a single premium for the entire group without knowing individual cancer histories, risk is not evenly spread, which may lead to adverse selection where more high-risk individuals (with family cancer history) purchase the insurance, potentially making it unprofitable for the insurer.