If the company charges this customer an annual premium of $270, what is the company's expected value of this insurance policy?

Question

Based on historical data, an insurance company estimates that a particular customer has a 3.2% likelihood of having an accident in the next year, with the average insurance payout being $2200.

If the company charges this customer an annual premium of $270, what is the company's expected value of this insurance policy?

Answer 1

This problem doesn't mention interest, so I'll ignore interest in this calculation.

The expected value of a policy is the average amount of money coming in minus the average amount of money going out.

The average amount of money going in is easy to calculate. The policy charges $270 at the beginning of the year, with certainty. The amount of money going in will ALWAYS be $270, so the average amount of money going in will be $270.

The average amount of money going out is a little bit harder to calculate. There's a 3.2% chance that there will be an accident with an average payout of $2200, which means there's a 96.8% chance that there is no accident, and therefore, no payout.

The average payout will be 0.968*0 (for the case where there is no accident) + 0.032 * $2200 (for the case where there is an accident).

Average money going out = 0.968*0 + 0.032*$2200 = $70.40

Now that we have the average money going out it is rather straightforward to calculate the average net earnings.

Average net earnings = Average money coming in - average money going out

Average net earnings = $270 - $70.40

Average net earnings = $169.60