b. What is the expected value for a 21-year-old male who buys the insurance? c.
ID: 3045090 • Letter: B
Question
b. What is the expected value for a 21-year-old male who buys the insurance?
c. What would be the cost of the insurance if the company just breaks even (in the long run with many suchpolicies), instead of making a profit?
d. Given that the expected value is negative (so the insurance company can make a profit), why should a21-year-old male or anyone else purchase life insurance?
An insurance company charges a 21-year-old male a premium of $250 for a one-year $50,000 life insurance policy. A 21-year-old male has a 0.999 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 dollars. The value if he dies isdollars.Explanation / Answer
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 = $99,750 dollars.
b. What is the expected value for a 21-year-old male who buys the insurance?
expected value = (-250)(0.999) + (99,750)(1 - 0.999) = -$150
The expected value is - $150 dollars.
c. 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?
(-x)(0.999) + (100,000 - x)(1 - 0.999) = 0
Now solve for x ...
x = $100
$100 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?
O Insuring the financial security of loved ones compensates for the negative expected values.
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