Question

Green, Inc., provides group term life insurance for all of its employees. The coverage equals twice the employee's annual salary. Sam, a vice president, worked all year for Green, Inc., and received $200,000 of coverage for the year at a cost to Green of $1,500. The Uniform Premiums (based on Sam's age) are $0.25 per month for $1,000 of protection. How much must Sam include in gross income this year

Answer 1

The actuarially fair premium for each group would be $2,000,000 for the group with a family history of cancer and $8,000,000 for the group without a family history of cancer. If the insurance company cannot find out about family cancer histories, the actuarially fair premium for the group as a whole would be $10,000,000. Charging the actuarially fair premium to the group as a whole rather than to each group separately may result in financial difficulties for the insurance company.

Step-by-step explanation:

In order to calculate the actuarially fair premium for each group, we need to consider the probability of dying and the amount of coverage.

For the group with a family history of cancer, 20% of the 1,000 men would have a one in 50 chance of dying. So, 200 men would have a chance of dying in the next year. The actuarially fair premium for this group would be the cost of insuring 200 men for $100,000, which is $2,000,000.

For the group without a family history of cancer, 80% of the 1,000 men would have a one in 200 chance of dying. So, 800 men would have a chance of dying in the next year. The actuarially fair premium for this group would be the cost of insuring 800 men for $100,000, which is $8,000,000.

If the insurance company were offering life insurance to the entire group without knowing their family cancer histories, they would have to use the weighted average of the probabilities of dying for both groups. The actuarially fair premium for the group as a whole would be the cost of insuring 1,000 men for $100,000, which is $10,000,000.

If the insurance company tries to charge the actuarially fair premium to the group as a whole rather than to each group separately, they may face financial difficulties. This is because they would be charging a higher premium to the group as a whole, which may discourage individuals from purchasing the insurance if they perceive it as unfair or too expensive.