Your company sells life insurance. You charge a 30 year old man $25 for a one ye

Question

Your company sells life insurance. You charge a 30 year old man $25 for a one year, $100,000 policy. If he dies over the course of the next year you pay out $100,000. If he lives, you keep the $25. Based on historical data (relative frequency approximation) the average 30 year old man has a 0.9999 probability of living through the year.

(a) What is your expected profit on this policy?
(b) What is the break-even price of such a policy?
I.e. What price should you charge to produce an expected profit of zero?

Explanation / Answer

a) Expected profit = 25x1 - 100,000x(1-0.9999)

= $415

b) Breakeven point is when expected profit = 0

Let the cost of policy be C

C = 100,000x(1-0.9999)

C = $10

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