Question

A new policyowner has a single-premium life insurance policy for which she paid $25,000 in premium. How often should the policyowner expect the interest rate to be applied to the cash value of the policy?

Answer 1

To calculate the actuarially fair premium for life insurance policies, multiply the probability of death by the payout amount. For individuals with a family history of cancer, the fair premium is $2,000, while for those without it is $500. Offering a uniform premium for all increases the risk of adverse selection and potential for a death spiral in policy ownership.

Step-by-step explanation:

The question posed involves determining the actuarially fair premiums for life insurance policies based on mortality risk and calculating the effect of charging a uniform premium to a diverse risk group. This is a standard calculation in actuarial science used by insurance companies to set fair premiums.

Calculation of Actuarially Fair Premium:

1. Identify the probability of death for each group: 1/50 for those with a family history of cancer (20% of 1,000 men) and 1/200 for those without (80% of 1,000 men).
2. Calculate the expected payout for each death: $100,000.
3. Multiply the probability by the payout to find the premium: (1/50 x $100,000) for the high-risk group and (1/200 x $100,000) for the low-risk group.
4. For the entire group, average the premium accounting for the 20% high risk and 80% low risk.

The actuarially fair premium for each sub-group would be:

• High-risk group: (1/50) x 100,000 = $2,000 per person
• Low-risk group: (1/200) x 100,000 = $500 per person

For the entire group, the actuarially fair premium would be:

(0.20 x $2,000) + (0.80 x $500) = $400 + $400 = $800 per person

Consequences of charging a uniform premium:

If the insurance company charges the fair premium to the group as a whole, the lower-risk individuals might consider the premium too high and choose not to purchase insurance, leading to adverse selection. This would leave the insurance company with a disproportionate number of high-risk individuals, requiring higher premiums to cover the increased likelihood of payouts, potentially leading to a cycle of increasing premiums and decreasing policy ownership (known as a 'death spiral').