November 7th, 2017, 04:10 AM  #1 
Senior Member Joined: Aug 2014 From: Mars Posts: 101 Thanks: 9  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. 
November 7th, 2017, 05:02 AM  #2  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,942 Thanks: 797  Quote:
Quote:
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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