Question

Blake died 20 days after his group life insurance coverage was terminated. He did not apply for individual coverage. Which of the following is true?

a. His beneficiary will not receive the death benefit because his group coverage was terminated.
b. His beneficiary will receive the death benefit minus the initial premium for the converted coverage.
c. His beneficiary will receive the full death benefit.
d. His beneficiary will receive 50% of the death benefit.

Answer 1

The actuarially fair premium would be $2,000 for men with a family history of cancer and $500 for those without. An average premium for a combined group would be $800. Charging an average premium could lead to adverse selection and potential losses for the insurance company.

Step-by-step explanation:

Calculating Actuarially Fair Premiums

When calculating the actuarially fair premium for life insurance, we assess the total expected payout and divide it by the number of policyholders. In the scenario with 50-year-old men divided into two groups based on their family history of cancer, we have two different risks for death and thus two separate premiums.

• Group with family history of cancer (20% of 1,000 men, 1 in 50 chance of dying): Expected death count is 20% of 1,000 * 1/50 = 4 deaths. The total expected payout is 4 * $100,000 = $400,000. The actuarially fair premium per person for this group would therefore be $400,000 / 200 (20% of 1,000) = $2,000.
• Group without family history of cancer (80% of 1,000 men, 1 in 200 chance of dying): Expected death count is 80% of 1,000 * 1/200 = 4 deaths. The total expected payout is 4 * $100,000 = $400,000. The actuarially fair premium per person for this group would therefore be $400,000 / 800 (80% of 1,000) = $500.

For the group as a whole, if the insurance company cannot distinguish between men with and without a family history of cancer, the risk is averaged across the entire group. The total expected payout would still be $800,000 (from both groups combined), and the premium would be $800,000 / 1,000 = $800 per person.

If the insurance company charges this average premium to everyone, those without a family history of cancer would be overpaying (since their actuarially fair premium is only $500), and those with a family history would be underpaying (since their actuarially fair premium is $2,000). This could lead to adverse selection, where the healthier group opts out of the insurance, leaving only the higher-risk individuals insured, which would eventually lead to losses for the insurance company.