Question 751101: Can some one walk me through this
An insurance company charges a 21-year old male a premium of $250 for a one year $100,000 life insurance policy. A 21 year old male has a 0.998 probability of living for a year.
a. From the perspective of a 21 year old male (or his estate), what are the values of the two different outcomes?
The value is he lives is [ ] dollars
The value if he dies is [ ] dollars
b. What is the expected value for a 21 year old male who buys the insurance?
The expected value is [ ] dollars
c. What would 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
d. 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?
[ ] A person who buys a one year policy will expect to make a profit
[ ] Insuring the financial security of loved ones compensates for the negative expected value
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An insurance company charges a 21-year old male a premium of $250 for a one year $100,000 life insurance policy. A 21 year old male has a 0.998 probability of living for a year.
a. 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 -250 dollars
The value if he dies is 100,000- 250 dollars
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b. What is the expected value for a 21 year old male who buys the insurance?
E(x) = 0.998(-250) + 0.002(100,000-250) = -50
The expected value is -50 dollars
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c. What would the cost of the insurance if the company just breaks even (in the long run with many such policies), instead of making a profit?
0.998x + 0.002(100,000-x] = 0
0.998x = 200 - 0.002x
x = $200 dollars
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d. 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?
[ ] A person who buys a one year policy will expect to make a profit
[x] Insuring the financial security of loved ones compensates for the negative expected value
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Cheers,
Stan H.
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