Question

Suppose a life insurance company sells a ​$250,000 ​one-year term life insurance policy to a 20​-year-old female for ​$320. The probability that the female survives the year is 0.999647. Compute and interpret the expected value of this policy to the insurance company.

Answer 1

The expected value is equivalent to the current receivable payment minus any potential payouts. The insurance company is assured of the $320 payment they will receive. Then the probability that the female will not survive the year is 1 - 0.999647 = 0.000353. We multiply this probability by the value of $250,000 to get $88.25. Then we subtract $320 - $88.25 to get the expected value of $231.75.