A 30 year old can buy $25,000 life insurance for $15/month. If the probability that the 30 year old will die is 0.14% find the insurance companies expected profit for the policy. (I want this in terms of their annual expectation-not monthly expectation)

To find the insurance company's expected profit for the policy in terms of their annual expectation, we need to calculate the annual revenue and annual costs.

First, let's calculate the annual revenue:
The monthly cost of the life insurance is $15. Therefore, the annual cost is $15/month * 12 months = $180.
To find the annual revenue, we multiply the annual cost by the number of policies sold. Since each policy costs $25,000, the number of policies sold is $25,000 / $180 = 138.89 (rounded to the nearest whole number). We can assume the insurance company sells 139 policies in a year (as you can't sell a fractional policy).

So, the annual revenue is $180/policy * 139 policies = $25,020.

Now, let's calculate the annual costs:
The probability that the 30-year-old will die is given as 0.14%. This means that out of 1000 people, 1.4 people are expected to die. We can assume the insurance company insures a large number of people, so we can use this probability as the expected number of death claims per year.

The amount paid out per death claim is $25,000. Therefore, the annual cost due to death claims is $25,000 * 1.4 = $35,000.

Finally, we can calculate the expected profit in terms of annual expectation:
Expected profit = Annual revenue - Annual costs
Expected profit = $25,020 - $35,000
Expected profit = -$9,980

Therefore, the insurance company has an expected loss of $9,980 in terms of their annual expectation for the policy.