suppose that a life insurance company insures 800,000 fifty year old people in a given year. (assume a death rate of 3 per 1000 people.) the cost of the premium is $500 per year, and the death benefit is $55,000. what is the expected profit or loss for the insurance company?

Answer 1

To calculate the expected profit or loss for the insurance company, we need to consider the number of deaths and the revenue from premiums and payouts.

Number of deaths:
Out of the 800,000 fifty-year-old people insured, the death rate is given as 3 per 1000 people. Therefore, the number of expected deaths can be calculated as follows:

Number of expected deaths = (800,000 / 1000) * 3 = 2,400

Revenue from premiums:
The premium for each insured person is $500, so the total revenue from premiums can be calculated as follows:

Total revenue from premiums = 800,000 * $500 = $400,000,000

Payouts for deaths:
Since the death benefit for each insured person is $55,000, the total payout for all expected deaths can be calculated as follows:

Total payouts for deaths = 2,400 * $55,000 = $132,000,000

Expected Profit or Loss:
The expected profit or loss is calculated by subtracting the total payouts for deaths from the total revenue from premiums:

Expected profit or loss = Total revenue from premiums - Total payouts for deaths
= $400,000,000 - $132,000,000
= $268,000,000

Therefore, the expected profit for the insurance company is $268,000,000.