An insurance company charges a 21-year-old male a premium of dollar 500 for a on

Question

An insurance company charges a 21-year-old male a premium of dollar 500 for a one-year dollar 50,000 life insurance policy A 21-year-old male has a 0 9985 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 dollars. The value if he dies is dollars. What is the expected value for a 21-year-old male who buys the insurance? The expected value is dollars. 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? Dollars Given that the expected value is negative (so the insurance company can make a profit), why should a 21-year-old male or anyone else purchase life insurance? Insuring the financial security of loved ones compensates for the negative expected value. A person who buys a one-year policy will expect to make a profit.

Explanation / Answer

Solution:-
a)The value if he lives is -500 dollars
The value if he dies is 50000 - 500 = 49500 dollars

b) E(x) = -500*0.9985 + 49500*0.0015
= -499.25 + 74.25
= -425
The expected value is -425 dollars

c) d*(1 - p) - (50000 - d)*p = 0 (no profit)

Hence the premium will be: d*(1 - p + p) = 5000*p = 75 dollars .   

d) option b. Insuring the financial security of loved ones compensates for the negative expected value
Explanation:-
A person who buys a one year policy does not expect to make a profit. In fact he expect to loose as shown under

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