An Automobile Insurance Company Estimates the Following Loss Probabilities for the Next

question 65

Essay

An automobile insurance company estimates the following loss probabilities for the next
year on a $25,000 sports car: $$\begin{array} { l l } \text { Total loss: } & 0.001 \\50 \% \text { loss: } & 0.01 \\25 \% \text { loss: } & 0.05 \\10 \% \text { loss: } & 0.10 \\\text { No loss: } & 0.839\end{array}$$ Assuming the company will sell only a $500 deductible policy for this model (i.e., the
owner covers the first $500 damage), how much annual premium should the company
charge in order to average $610 profit per policy sold?

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Definitions:

Depreciation

The structured apportioning of the price of a tangible asset across its operational life.

Sales Commissions

Payments made to salespersons or agents based on the sales they generate.

Product Costs

All costs incurred to acquire or produce the finished products that are sold to customers.

Income Statement

A financial statement that reports a company's financial performance over a specific accounting period, detailing revenues, expenses, and profits or losses.