Yosef T. answered • 02/19/20
RPI Ph.D. Math/Physics Tutor with a passion for teaching
The problem doesn't mention an interest rate, so I'll ignore interest.
Suppose the company sells one such policy. The policy is sold for $5000, according to the problem. This means that, with certainty, the insurance company gets $5000. The question is this: On average, how much money will they have to pay back in insurance claims at the end of the year?
The problem states that a 25-year-old man has a 90% chance of surviving the year. This means that a 25-year-old man would have a 10% chance of dying this year, when the policy is still in effect. (Note, this 10% probability of death is VERY unrealistic. The actual probability of death is closer to 0.1%)
According to the probabilities given in the problem, there is a 10% chance that the company will have to pay out $40,000, and a 90% chance that they won't have to pay anything. (You don't have to pay life insurance benefits for someone who isn't dead.) This means that their average death benefit payout is only 10% of $40,000, or $4,000.
The average earnings is equal the the average money coming in minus the average money going out.
Average earnings = $5000 - $4,000 = $1,000
That's $5,000 coming in from selling the policy minus the average of $4,000 going out at the end of the year in death benefits, leaving earnings of $1,000.
