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Chapter 11: Problem 8

A 25 -year-old can purchase a one-year life insurance policy for \(\$ 10,000\) at a cost of \(\$ 100\). Past history indicates that the probability of a person dying at age 25 is \(0.002\). Determine the company's expected gain per policy.

Short Answer

Expert verified
The company's expected gain per policy is \$80.

Step by step solution

01

Calculate Expected Payout Cost

First, calculate the expected payout by the company, which is the product of the potential payout (\$10,000) and the probability of the payout (\(0.002\)). This gives:\[Expected \, payout \, cost = \$10,000 * 0.002 = \$20\]
02

Calculate income from the policy

The company always receives the cost of the policy (\$100), regardless of whether the person dies or not. So, the income from the policy is:\[Income \, from \, policy = \$100\]
03

Calculate Expected Gain

Finally, calculate the company's expected gain per policy by subtracting the expected payout cost from the income from the policy. This gives:\[Expected \, gain = Income \, from \, policy - Expected \, payout \, cost = \$100 - \$20 = \$80\]

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