Which answer is correct? 1 or 2? Can you please help me solve this? Life Insuran

Question

Which answer is correct? 1 or 2? Can you please help me solve this?

Life Insurance: 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?

1.

(a) Expected profit = 25x1 - 100,000x(1-0.9999) = $415

(b)  Breakeven point is when expected profit = 0

I.e. What price should you charge to produce an expected profit of zero?

100,000x(1-0.9999) = $10

2.

(a).

outcomes    profit= x   p(x) x*p(x)

lives        25 0.9999    24.9975

dies   -99975 0.0001      -9.9975  

add the 24.9975+(-9.9975)=15 is the expected profit  

(b.) the break-even is 10

I got that by calculating if his payment of 25 subtracting the expected income of 15 and getting 10.

when factoring it in a similar table as above it comes to zero.

Explanation / Answer

The second answer is correct.

(a) Calculated correctly, nothing to add. As a rule, the expected value = X * P(X)

(b) Let I be the premium to be charged to arrive at the expected profit = 0

Then I x 0.9999 + (-100000+25) x 0.0001 = 0

I x 0.9999 = 9.9975

So I = 9.9975 / 0.9999 = 9.9985.

This is close the $ 10 mentioned in the answer, but $10 as the answer is not fully correct. The correct answer should be $ 9.9985

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