Jim has a 5-year-old car in reasonably good condition. He wants to take out a $50,000 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 charges $7000 for the policy, how much profit does the company expect to make? Round your answer to the nearest dollar.
$$\begin{array} { l c c c c c }
x = \text { age } & 5 & 6 & 7 & 8 & 9 \
P \text { (accident) } & 0.01182 & 0.01282 & 0.01386 & 0.01513 & 0.01602
\end{array}$$
A)$3515
B)$3520
C)$3513
D)$3522
E)$3518

Question

Jim has a 5-year-old car in reasonably good condition. He wants to take out a $50,000 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 charges $7000 for the policy, how much profit does the company expect to make? Round your answer to the nearest dollar.
$$\begin{array} { l c c c c c } 
x = \text { age } & 5 & 6 & 7 & 8 & 9 \
P \text { (accident) } & 0.01182 & 0.01282 & 0.01386 & 0.01513 & 0.01602
\end{array}$$
A)$3515
B)$3520
C)$3513
D)$3522
E)$3518

Quizplus · Accepted Answer

To calculate the expected profit for the insurance company, we first need to calculate the expected payout for each year and then sum these up to find the total expected payout over the 5 years. The profit is then the premium charged minus this total expected payout.For each year, the expected payout is the probability of an accident times the payout in the event of an accident ($50,000).1. Year 5: $0.01182 \times 50,000 = 591$2. Year 6: $0.01282 \times 50,000 = 641$3. Year 7: $0.01386 \times 50,000 = 693$4. Year 8: $0.01513 \times 50,000 = 756.5$5. Year 9: $0.01602 \times 50,000 = 801$Adding these up gives the total expected payout: $591 + 641 + 693 + 756.5 + 801 = 3482.5$.The insurance company charges $7000 for the policy, so the expected profit is $7000 - 3482.5 = 3517.5$, which rounds to $3518.

Jim Has a 5-Year-Old Car in Reasonably Good Condition A)$3515 B)$3520 C)$3513 D)$3522 E)$3518

Jim Has a 5-Year-Old Car in Reasonably Good Condition A)$3515
B)$3520
C)$3513
D)$3522
E)$3518