An automobile insurance company estimates the following loss probabilities for the nextyear 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 $565 profit per policy sold?

Question

An automobile insurance company estimates the following loss probabilities for the nextyear 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 $565 profit per policy sold?

Quizplus · Accepted Answer

The Answer of An automobile insurance company estimates the following loss probabilities for the nextyear 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 $565 profit per policy sold?

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