A 20-year-old male purchases a 1-year life insurance policy worth 250,000 dollars. The insurance company determines that he will survive the policy period with probability 0.9988.

(a) If the premium for the policy is 400 dollars, what is the expected profit for the insurance company?

(b) At what value should the company set its premium so its expected profit will be 220 dollars per policy for 20-year-old males?

Question

A 20-year-old male purchases a 1-year life insurance policy worth 250,000 dollars. The insurance company determines that he will survive the policy period with probability 0.9988.

(a) If the premium for the policy is 400 dollars, what is the expected profit for the insurance company?

(b) At what value should the company set its premium so its expected profit will be 220 dollars per policy for 20-year-old males?

dumbcow · Answer

E(x) = p*x - (1-p)*250,000, where x is the premium and p is probability of survival
For part a) substitute 400 for x and .9988 for p and calculate E(x) the expected profit
For part b) substitute 220 for E(x) and solve for x
Hope this helps