Question

The probability that a 30-year-old male in the U.S. will die within one year is about 0.00142. An insurance company is preparing to sell a 30-year-old male a one-year, $40,000 life insurance policy. How much should it charge for its premium in order to have a positive expectation for the policy? (Round your answer to the nearest dollar.)

Answer 1

P(dying) = 0.00142

Let say the premium be $x.

P(company's profit of $x) = P(not dying) = 1 - 0.00142 = 0.99858

P(company's loss $(40000 - x)) = P(dying) = 0.00142

E(X) = 0

or, x * 0.99858 - (40000 - x) * 0.00142 = 0

or, x = 56.8

or, x = $57