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 $25,000 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?