Question

Avicenna, a major insurance company, offers five-year life insurance policies to 65-year-olds. If the holder of one of these policies dies before the age of 70, the company must pay out $26,500 to the beneficiary of the policy, Executives at Avicenna are considering offering these policies for $497 each. Suppose that for each holder of a policy there is a 2% chance that they will die before the age of 70 and a 98% chance they will live to the age of 70.

If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much?
To answer, take into account the price of the policy and the expected value of the amount paid out to the beneficiary.
Avicenna can expect to make money from offering these policies. In the long run, they should expect to make _________ dollars on each policy sold,
Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose ________ dollars on each policy sold
Avicenna should expect to neither make nor lose money from offering these policies.

Answer 1

Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose ___33__ dollars on each policy sold

Explanation:

Given :

The amount the company Avicenna must pay to the shareholder if the person die before 70 years = $ 26,500

The value of each policy = $497

It is given that there is a 2% chance that people will die before 70 years and 98% chance that people will live till the age 70.

The expected policy to be sold= policy nominal + chances of death

= 497 + [98% (no pay) + 2% (pay)]

= 497 + [98%(0) + 2%(-26500)]

(The negative sign shows that money goes out of the company)

= 497 - 2% (26500)

= 497 - 530

=33

Therefore the company loses 33 dollar on each policy sold in the long run.