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2 votes
Suppose a life insurance company sells a

$280,000
1-year term life insurance policy to a
20-year-old
female for
$270.
According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is
0.999544.
Compute and interpret the expected value of this policy to the insurance company.

User Lye Fish
by
7.9k points

1 Answer

4 votes

Answer:

$142.32, profit on sale of the policy

Explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

Cost

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

0.000456 × $280,000 = $127.68

Profit

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

$270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

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Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

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User Danharaj
by
8.3k points