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November 7th, 2017, 04:10 AM   #1
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Solving for X

How do I solve?


If an insurance company wants to make an average of 16% of the total policy cost (to the customer) on each of its insurance policies. Someone wants insurance for a painting worth \$7574 and a vase worth \$7762. In a given year the insurance company estimates that the probability the painting will need to be replaced is 0.0073, and the probability that the vase will need to be replaced is 0.0062. If the insurance company believes that in a given year the probability of the painting or the vase will need to be replaced is 0.0102 what should the yearly insurance premium be?

The answer is 123.11. But I don't know how they got this answer.

Last edited by greg1313; November 7th, 2017 at 05:02 AM.
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November 7th, 2017, 05:02 AM   #2
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Originally Posted by Opposite View Post
How do I solve?


If an insurance company wants to make an average of 16% of the total policy cost (to the customer) on each of its insurance policies. Someone wants insurance for a painting worth \$7574 and a vase worth \$7762.
On this board dollar signs are interpreted as beginning and ending latex. I put "\" before each \$.

Quote:
In a given year the insurance company estimates that the probability the painting will need to be replaced is 0.0073, and the probability that the vase will need to be replaced is 0.0062. If the insurance company believes that in a given year the probability of the painting or the vase will need to be replaced is 0.0102 what should the yearly insurance premium be?

The answer is 123.11. But I don't know how they got this answer.
There is a 0.0073 probability the painting will need to be replaced in which case the insurance company would have to pay \$7574. The average cost to the insurance company is (0.0073)(7574)= \$55.29 per year. There is a 0.0062 probability the vase will need to be replaced in which case the insurance company will have to pay \$7762. The average cost to the insurance company is (0.0062)(7762)= \$48.12.

That is, the insurance company will have to charge 55.29+ 48.12= \$103.41 annually just to "break even". But the insurance company wants to make a profit of 16% of the premium. If the premium is S then the insurance company wants to make a profit of 0.16S.

The annual premium must be that "break even" amount plus the profit so we must have S= 0.16S+ 103.41. Subtracting 0.16S from both sides, S- 0.16S= 0.84S= 103.41. Divide both sides by 0.84 to get S= 103.41/0.84= \$123.11.
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