SOLUTION: Suppose a life insurance company sells a $190,000 one year term life insurance policy to a 25- year old female for $370. The probability that the female survives the year is 0.999
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Question 1167865: Suppose a life insurance company sells a $190,000 one year term life insurance policy to a 25- year old female for $370. The probability that the female survives the year is 0.999536. Compute and interpret the expected value of this policy to the insurance company.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the woman does not survive the year, the company pays out 190,000 dollars.
if the woman survives the year, the company keeps the 370 dollars and pay out nothing.
the probability that the woman survives the year is .999536.
the probability that the woman doesn't survive the year is 1 minus that = .000464.
the expected value is 370 - .000464 * 190,000 = 281.84 dollars.
the company gets 370 from everybody who buys that same policy and the company pays out 190,000 for anybody who does not survive the year.
this is how it works.
suppose the company sold the same policy to 1 million 25 year old females.
the company collects 1 million * 370 = 370 million dollars.
.000464 * 100 = .0464% of the females die within the year.
that would be .000464 * 1 million = 464 females who bought the policy that do not survive the year.
the company pays out 464 * 190,000 = 88.160 million dollars.
the company net revenue for the year = 370 million minus 88.160 million = 281.84 million.
divide that by 1 million customers and you get average net revenue of 281.84 per customer.
that's the expected value for each customer.
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