Question

Insurance companies use age 100 to calculate life insurance death benefits because:

A. They assume everyone will have died by that age
B. It makes sure they never have to pay a death benefit
C. They assume that mortality rates will decrease by then
D. It allows them to charge higher premiums

Answer 1

Life insurance premiums are calculated using actuarial science to assess risk. In this example, different premiums would be set for men with and without a family history of cancer based on their mortality risk, and the insurance company could face financial losses if it charges a uniform premium to a mixed-risk group due to adverse selection.

Step-by-step explanation:

When an insurance company sells life insurance, they calculate premiums based on actuarial science, which incorporates statistics and probability to estimate risk. This example involves dividing 50-year-old men into two groups based on family history of cancer to establish different mortality risks.

For men with a family history of cancer (20% or 200 out of 1000):
Probability of dying in the next year = 1/50
Expected deaths = 200 * (1/50) = 4
Total payout on expected deaths = 4 * $100,000 = $400,000
Actuarially fair premium = $400,000 / 200 = $2,000 per person

For men without a family history of cancer (80% or 800 out of 1000):
Probability of dying in the next year = 1/200
Expected deaths = 800 * (1/200) = 4
Total payout on expected deaths = 4 * $100,000 = $400,000
Actuarially fair premium = $400,000 / 800 = $500 per person

Total expected deaths = 4 (from cancer history group) + 4 (from non-cancer history group) = 8
Total payout on expected deaths = 8 * $100,000 = $800,000
Actuarially fair premium for the entire group = $800,000 / 1000 = $800 per person

If the insurance company charges the entire group the actuarially fair premium of $800, there is a risk of adverse selection. Those with higher risk (family history of cancer) are more likely to buy the insurance since they would be undercharged relative to their risk (paying $800 instead of the fair $2,000). Simultaneously, those with lower risk (no family history of cancer) might opt out of buying insurance since they would be overcharged (paying $800 instead of the fair $500). This could lead to a pool of insured individuals with higher overall risk, making the premium insufficient to cover the death benefits, and the company could face financial losses.