Question

Expected Value for Life Insurance There is a 0.9986 probability that a randomly selected 30-year-old male

lives through the year (based on data from the U.S Department of Health and Human Services). A Fidelity life
insurance company charges $161 for insuring that the male will live through the year. If the male does not survive
the year, the policy pays out $100,000 as a death benefit
I
a. From the perspective of the 30-year-old male, what are the monetary values corresponding to the two
events of surviving the year and not surviving?
b. Ifa 30-year-old male purchases the policy, what is his expected value?
c. Can the insurance company expect to make a profit from many such policies? Why?

Answer 1

Answer and Explanation:

a. If the 30-year-old male survives the year, he will have paid the insurance company $161 and not received any additional payment. If he does not survive the year, he will have paid $161 and his beneficiary will receive a payment of $100,000.

b. To calculate the expected value, we multiply the probability of each event by its corresponding monetary value and sum the results:

Expected value = (0.9986 × $161) + (0.0014 × -$99,839)

Expected value = $160.68 - $139.79

Expected value = $20.89

Therefore, the expected value for the 30-year-old male is $20.89.

c. Yes, the insurance company can expect to make a profit from many such policies. The expected value for the 30-year-old male is positive, meaning that on average, the insurance company will collect more in premiums than it pays out in benefits. The insurance company is able to make a profit by using actuarial tables and statistical analysis to accurately predict the likelihood of different events occurring and setting premiums accordingly.