Questions: If a 60 year-old buys a 1000 life insurance policy at a cost of 50 and has a probability of 0.977 of living to age 61, find the expectation of the policy until the person reaches 61. Round your answer to the nearest cent. The expectation of the policy until the person reaches 61 is dollars.

If a 60 year-old buys a 1000 life insurance policy at a cost of 50 and has a probability of 0.977 of living to age 61, find the expectation of the policy until the person reaches 61. Round your answer to the nearest cent.

The expectation of the policy until the person reaches 61 is dollars.

Transcript text: If a 60 year-old buys a $\$ 1000$ life insurance policy at a cost of $\$ 50$ and has a probability of 0.977 of living to age 61 , find the expectation of the policy until the person reaches 61. Round your answer to the nearest cent. The expectation of the policy until the person reaches 61 is $\square$ dollars.

Solution

Solution Steps

Step 1: Calculate the Expected Payout if the Person Lives

The expected payout if the person lives is 0 because the insurance does not pay out. However, the cost of the policy is lost. Thus, this part of the expectation is negative and equals the cost of the policy (C), which is $50.

Step 2: Calculate the Expected Payout if the Person Dies

This is calculated as the payout of the policy (P) minus the cost of the policy (C), weighted by the probability of dying (1 - L). Expected if dies = (P - C) * (1 - L) = ($1000 - $50) * (1 - 0.977) = $21.85.

Step 3: Combine the Two Expectations

The total expectation (E) can be calculated as: E = P * (1 - L) - C. After simplifying, we get: E = $1000 * (1 - 0.977) - $50 = $-27.