Question 759149: Not really sure where to start with this problem. Thank you in advance for your help.
An insurance company changes 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 0.998 probability of living a year.
From the prospective of a a 21-year-old (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 instead of making a profit?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The value if he lives is __-250__ dollars.
This is the amount he loses in a year if he doesn't die and doesn't get the $50,000 payout.
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The value if he dies is __50,000__ dollars. Note: obviously he doesn't benefit if he's dead (his family/estate does).
This is the amount that gets paid out to the family/estate if he dies.
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Note: P(living) = "probability of living" and V(dying) = "value of dying" (see above)
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] = 0.998*(-250) + (1-0.998)*(50,000)
E[X] = -149.5
The expected value is __-149.50__ dollars.
This is the amount, on average, the policy holder expects to lose each year.
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What would be the cost of the insurance if the company just breaks even instead of making a profit?
Let x = cost of insurance (ie the premiums paid per year)
If the company breaks even, they will not lose money and they will not profit.
So if the company breaks even, then they expect to get $0 on average, so E[X] = 0.
E[X] = P(living)*V(living) + P(dying)*V(dying)
0 = 0.998*(x) + (1-0.998)*(50,000)
0 = 0.998*(x) + (0.002)*(50,000)
0 = 0.998*(x) + 100
-100 = 0.998*x
0.998*x = -100
x = -100/0.998
x = -100.200400801603
x = -100.20
x is negative because this is from the viewpoint of the policyholder (he loses this much every year when making the premium payment)
So the cost of insurance is roughly $100.20 every year if the company just breaks even instead of making a profit
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