An insurance company charges a 21-year-old male a premium of $500 for a one-year

Question

An insurance company charges a 21-year-old male a premium of $500 for a one-year $ 50000 life insurance policy. A 21-year-old male has a 0.999 probability of living for a year.

From the perspective of a 21-year-old male (or his estate), what are the values of the two different outcomes?

the value if he lives is x dollar?

the value if he dies is x dollar?

What is the expected value for a 21-year-old male who buys the insurance?

What would be the cost of the insurance if the company just breaks even (in the long run with many such policies), instead of making a profit?

Explanation / Answer

the value if he lives is x dollar?

if he lives , then he losses the money on the insurance which is -500

the value if he dies is x dollar?

if he dies , then the value is 50000 dollars , as he gets the insurance

What is the expected value for a 21-year-old male who buys the insurance?

E[X] = P(living)*V(living) + P(dying)*V(dying)

E[X] = 0.999*(-500) + (1-0.999)*(50000)

E[X] = -449.5

What would be the cost of the insurance if the company just breaks even (in the long run with many such policies), instead of making a profit?

breaking even means no loss no gain , so Ex becomes zero

so E[X] = 0.

E[X] = P(living)*V(living) + P(dying)*V(dying)

0 = 0.999*(x) + (1-0.999)*(50000)

0 = 0.999*(x) + (0.001)*(50,000)

0 = 0.999*(x) + 50

-50 = 0.999*x

x = -50/0.999

x = -50.05 , negative sign implies that the policy holder looses this money every year

hope this helps !!

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