A private pilot wishes to insure his airplane for$200,000. The insurance company estimates that a total loss will occur with probability 0.002, a 50% losswith probability 0.01, and a 25% loss with probability 0.1. Ignoring all other partial losses, what premium should the insurance company charge each year to realize an average profit of $500?

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Leblanc

14 June, 05:10

A private pilot wishes to insure his airplane for$200,000. The insurance company estimates that a total loss will occur with probability 0.002, a 50% losswith probability 0.01, and a 25% loss with probability 0.1. Ignoring all other partial losses, what premium should the insurance company charge each year to realize an average profit of $500?

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Isabel Harmon · Answer 1

The answer is: $6,900

Explanation:

To determine how much the insurance company should charge, we must first calculate the amount of money they expect to pay:

total loss $200,000 x 0.002 = $400 50% loss $100,000 x 0.01 = $1,000 25% loss $50,000 x 0.1 = $5,000

Total $6,400

If the insurance company expects to pay $6,400 per year, they will have to charge $6,900 ($6,400 + $500) to cover their expenses and earn a $500 profit.