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

Essay

An automobile insurance company estimates the following loss probabilities for the next year on a $25,000sports car: $$\begin{array} { l r } \text { Total loss: } & 0.001 \\50 \% \text { loss: } & 0.01 \\25 \% \text { loss: } & 0.05 \\10 \% \text { loss: } & 0.10\end{array}$$ 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 $325 profit perpolicy sold?