Final answer:
The statement regarding Tom shopping for a joint policy that pays only when the first person dies is false. Actuarially fair premiums for men with or without a family history of cancer would be $2,000 and $500 respectively.
Step-by-step explanation:
Life Insurance Policy Types and Premium Calculations
Tom is shopping for a policy that would pay out the face amount when the first person dies. The type of life policy he is looking for is false to be a joint life policy.
A joint life policy is actually designed to pay out upon the death of one of the insured parties, but the question is phrased in a way that suggests it pays only upon the first death. This is not characteristic of joint life policies, which continue to cover the surviving party.
To calculate the actuarially fair premium for a group of 1,000 50-year-old men, divided into two groups based on family cancer history, we would have to consider their respective probabilities of dying within the next year.
20% with a family history of cancer having a 1 in 50 chance and the remaining 80% with a 1 in 200 chance.
a. For the group with a family history of cancer (200 men), the fair premium would be calculated as: (1/50 chance of dying) x ($100,000 death benefit) x 200 people = $400,000. The premium per person is $400,000/200 = $2,000.
For the group without a family history of cancer (800 men), the premium is: (1/200 chance of dying) x ($100,000) x 800 people = $400,000. The premium per person here is $400,000/800 = $500.
b. If selling to the entire group without knowledge of cancer history, the premium for the entire group would be the total risk, $800,000, divided by the whole group of 1,000 men, resulting in a fair premium of $800 per person.
c. If the insurance company charges the actuarially fair premium to the entire group, those with a higher risk (family history of cancer) would benefit, while those at lower risk would be overpaying.
Consequently, the lower-risk group may choose to leave the pool, leading to adverse selection and potential insolvency for the insurance company, as they would be left with a pool of high-risk individuals.