Question

Life Insurance: Your company sells life insurance. You charge a 30 year old man $25 for a one year, $100,000 policy. If he dies over the course of the next year you pay out $100,000. If he lives, you keep the $25. Based on historical data (relative frequency approximation) the average 30 year old man has a 0.9999 probability of living through the year. (a) What is your expected profit on this policy?

Answer 1

Given:

• Insurance amount = $25

,

• Expected payout = $100,000

,

• Probability = 0.9999

Let's find the expected payout.

To find the expected payout, apply the formula:

Expected profit = (Insurance amount x probability the man lives) + (-expected payout x probability the man dies)

Where:

Probability the man dies = 1 - 0.9999 = 0.0001

Thus, we have:

Expected profit = (25 x 0.9999) + (-100000 x 0.0001)

Expected profit = 24.9975 - 10

Expected profit = 14.9975 ≈ 15

Therefore, the expected profit is $15

• ANSWER:

$15