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## Can you help with this math problem?

### Can you help with this math problem?

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.
camille

Posts: 396
Joined: Fri Apr 01, 2011 7:02 pm

### Can you help with this math problem?

P - 0.03*30,000 = 0
P = \$900
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branduff

Posts: 421
Joined: Thu Mar 31, 2011 4:31 pm

### Can you help with this math problem?

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
bercleah

Posts: 458
Joined: Thu Mar 31, 2011 1:43 am