Jim has a 5-year-old car in reasonably good condition. He wants to take out a $60,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows: Jim is applying to a car insurance company for his car insurance policy. If the car insurance company wants to make a profit of $800 above the expected total losses of $4179, how much should it charge for the policy?
$$\begin{array} { l c c c c c }
x = \text { age } & 5 & 6 & 7 & 8 & 9 \
P \text { (accident) } & 0.01182 & 0.01282 & 0.01386 & 0.01513 & 0.01602
\end{array}$$
A)$4977
B)$4969
C)$4989
D)$4979
E)$4981

Question

Jim has a 5-year-old car in reasonably good condition. He wants to take out a $60,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows: Jim is applying to a car insurance company for his car insurance policy. If the car insurance company wants to make a profit of $800 above the expected total losses of $4179, how much should it charge for the policy?
$$\begin{array} { l c c c c c } 
x = \text { age } & 5 & 6 & 7 & 8 & 9 \
P \text { (accident) } & 0.01182 & 0.01282 & 0.01386 & 0.01513 & 0.01602
\end{array}$$
A)$4977
B)$4969
C)$4989
D)$4979
E)$4981

Quizplus · Accepted Answer

To calculate the premium the insurance company should charge, we first need to determine the expected total losses over the 5-year period. This is done by multiplying the probability of an accident each year by the payout amount ($60,000), and then summing these values for each year from 5 to 9.Expected loss for year 5: $60,000 * 0.01182 = $709.20Expected loss for year 6: $60,000 * 0.01282 = $769.20Expected loss for year 7: $60,000 * 0.01386 = $831.60Expected loss for year 8: $60,000 * 0.01513 = $907.80Expected loss for year 9: $60,000 * 0.01602 = $961.20Total expected losses over 5 years = $709.20 + $769.20 + $831.60 + $907.80 + $961.20 = $4179The insurance company wants to make a profit of $800 above the expected total losses. Therefore, the total amount it should charge for the policy is:$4179 (expected losses) + $800 (desired profit) = $4979Thus, the insurance company should charge $4979 for the policy.

Jim Has a 5-Year-Old Car in Reasonably Good Condition A)$4977 B)$4969 C)$4989 D)$4979 E)$4981

Jim Has a 5-Year-Old Car in Reasonably Good Condition A)$4977
B)$4969
C)$4989
D)$4979
E)$4981