Final answer:
A Straight Life policy has a level annual premium. Actuarially fair premiums for groups with different risk levels are calculated based on expected payouts, with those at higher risk paying more. An insurance company may face financial risks if it cannot set premiums based on individual risk levels.
Step-by-step explanation:
The answer to the student's question is D - A level annual premium for the life of the insured. A Straight Life policy, also known as a Whole Life policy, features a premium that does not change throughout the life of the policy. This means the policyholder pays the same amount every year.
Now let's explore the example scenario:
- For men with a family history of cancer (20%), the probability of death within a year is 1/50. To find the actuarially fair premium, we calculate the expected payout, which is $100,000 divided by 50. This provides an actuarially fair premium of $2,000 for this group.
- For men without a family history of cancer (80%), the probability of death within a year is 1/200. Therefore, the expected payout would be $100,000 divided by 200, resulting in an actuarially fair premium of $500 for this group.
- If the insurance company were forced to combine the two groups and set a single premium, they would need to find a weighted average. Considering the differing probabilities, this single actuarially fair premium would, out of necessity, be somewhere between those calculated separately for each group.
- However, if the insurance company charges the whole group the same premium, it risks adverse selection where individuals with a higher risk are more likely to purchase insurance, potentially resulting in financial losses for the company if the premium does not adequately cover the higher probability of claims.
A cash-value or whole life insurance policy provides both a death benefit and a cash value, which accumulates over time and can serve as an account for the policyholder's use.