Suppose a life insurance company sells a $300,000 one-year term life insurance p

Question

Suppose a life insurance company sells a $300,000 one-year term life insurance policy to a 19 -year-old female for $180. The probability that the female survives the year is 0.999476. Compute and interpret the expected value of this policy to the insurance company.

The expected value is $______.

(Round to two decimal places as needed.)

Which of the following interpretation of the expected value is correct?

A. The insurance company expects to make an average profit of $2.07 on every 19-year-old female it insures for 1 month.

B. The insurance company expects to make an average profit of $22.80 on every 19-year-old female it insures for 1 year.

C. The insurance company expects to make an average profit of $16.36 on every 19-year-old female it insures for 1 month.

D. The insurance company expects to make an average profit of $179.91 on every 19-year-old

female it insures for 1 year.

Explanation / Answer

Let the S be value of this policy to the insurance company

Survivied non Survivied

S 180 -300000+180=-2,99,820

Prob.   0.999476 0.000524

The expected value of this policy to the insurance company

E(S) = 180 * 0.999476 - 299820*0.000524 = 179.90568 - 157.10568 = 22.8

Correct Answer: B. The insurance company expects to make an average profit of $22.80 on every 19-year-old female it insures for 1 year.

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