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?
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.