An insurance company offers to sell you a life insurance policy which will pay y
ID: 3183451 • Letter: A
Question
An insurance company offers to sell you a life insurance policy which will pay your beneficiary $100,000 if you die. They estimate that the probability that you will die in the next year is 0.00056. If the company wants to expect to make a profit on the policy, then how much do they have to charge per year?I'm not looking for the expected value of this policy, but for how much the company should charge per year if they want to make a profit. An insurance company offers to sell you a life insurance policy which will pay your beneficiary $100,000 if you die. They estimate that the probability that you will die in the next year is 0.00056. If the company wants to expect to make a profit on the policy, then how much do they have to charge per year?
I'm not looking for the expected value of this policy, but for how much the company should charge per year if they want to make a profit.
I'm not looking for the expected value of this policy, but for how much the company should charge per year if they want to make a profit.
Explanation / Answer
Let the company charge $x. Then,
P(Dying) = 0.00056
P(Surviving) = 1 - P(Dying) = 1 - 0.00056 = 0.99944
Amount gained by company in case of person survival = x
Amount loss by company in case of person dying = - (100000 - x)
Hence,
Expected value
= x(0.99944) - (100000 - x)(0.00056)
= x - 56
For x - 56 > 0
x > 56
So,
The company should charge greater than $56 in order to make the profit.
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