Question

M has an annual life insurance premium payment due January 1. She died January 19 without making the premium payment. What action will the insurer take?

a. Collect premium from M's estate
b. Deny the claim
c. Pay face amount minus the past due premium
d. Subtract past due premium from cash value

Answer 1

If the insurance company were selling life insurance separately to each group, the actuarially fair premium for each group would be $25,000. If the insurance company were offering life insurance to the entire group without knowing about family cancer histories, the actuarially fair premium for the group as a whole would be $2,500,000. If the insurance company tried to charge the actuarially fair premium to the group as a whole rather than to each group separately, it could face financial losses due to adverse selection.

Step-by-step explanation:

If the insurance company were selling life insurance separately to each group, the actuarially fair premium for each group could be calculated as follows:

1. For the group with a family history of cancer: 20% of the 1,000 men, which is 200 men, have a one in 50 chance of dying in the next year. So, the expected number of deaths for this group would be 200/50, which is 4. The actuarially fair premium for this group would be $100,000/4, which is $25,000.
2. For the group without a family history of cancer: 80% of the 1,000 men, which is 800 men, have a one in 200 chance of dying in the next year. So, the expected number of deaths for this group would be 800/200, which is 4. The actuarially fair premium for this group would also be $100,000/4, which is $25,000.

If the insurance company were offering life insurance to the entire group without knowing about family cancer histories, there would be no way to differentiate the groups. Therefore, the actuarially fair premium for the group as a whole would be calculated based on the overall probability of dying in the next year. The overall chance of dying for the entire group would be (20%*1/50) + (80%*1/200), which is 0.04. The actuarially fair premium for the group as a whole would be $100,000/0.04, which is $2,500,000.

If the insurance company tried to charge the actuarially fair premium to the group as a whole rather than to each group separately, it would be charging the same premium to both the higher-risk group and the lower-risk group. This could lead to adverse selection, where individuals in the higher-risk group are more likely to purchase insurance, leading the insurance company to pay out more claims than anticipated. As a result, the insurance company may face financial losses.