Question

The probability that a 80-year-old female in the U.S. will die within one year is about 0.048711. An insurance company is preparing to sell a 80-year-old female a one-year, $30,000 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

Answer:

$1,461

Explanation:

P(80-year-old female in the U.S. will die within 1 year) = 0.048711.

P(80-year-old female in the U.S. will survive one year) = 1 - 0.048711

P(80-year-old female in the U.S. will survive one year) = 0.951289

If 80-year-old female dies within one year, company will lose $(75000-x) but if she will survive, the company will make $x where x is the charge for its premium.

x(0.951289) - (30,000-x)0.048711 > 0

=> 0.951289x + 0.048711x - 30,000(0.048711) > 0

=> 1x - 1461.33> 0

=> x > 1461.33

=> x > 1461

x = $1,461