An insurance company will insure a $75,000 Hummer for its full value against theft at a premium of $1500 per year.Suppose that the probability that the Hummer will be stolen is 0.0075.Find the premium that the insurance company should charge if it wants its expected net profit to be $2000.
A)$1437.50
B)$2551.25
C)$2562.50
D)$2062.50

Question

Quizplus · Accepted Answer

The expected net profit for the insurance company can be calculated as follows:
Expected net profit = Premium - (Probability of theft * Value of Hummer)
We know that the value of the Hummer is $75,000, the probability of theft is 0.0075, and the expected net profit should be $2,000. We can use this information to solve for the premium that the insurance company should charge:
2000 = Premium - (0.0075 * 75000)
2000 = Premium - 562.50
Premium = 2562.50
Therefore, the insurance company should charge a premium of $2562.50 to achieve its expected net profit of $2000. The correct answer is C.

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