A man wishes to purchase a 5-year term-life insurance policy that will pay the beneficiary $30,000 in the event that the man's death occurs during the next 5 years. Using life insurance tables, he determines that the probability that he will live another 5 years is 0.97. What is the minimum amount that he can expect to pay for his premium? Hint: The minimum premium occurs when the insurance company's expected profit is zero.

P - 0.03*30,000 = 0
P = $900
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Pamela -

The amount of money the insurance company will pay out is 30000 if someone dies. They receive the premium P regardless if the person lives or dies.

So here is the "expected" formula to solve for P:

(P - 30000)(1-0.97) + (P)(0.97) = 0

0.03P - 900 + 0.97P = 0

P = $900 is the minimum amount that he can expect to pay for his premium.

Hope that helps