Jim has a 5-year-old car in reasonably good condition. He wants to take out a $30,000 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:

Question

x = age
5
6
7
8
9

P (accident)
0.01191
0.01292
0.01396
0.01503
0.01613


Jim is applying to a car insurance company for his car insurance policy. If the car insurance company wants to make a profit of $900 above the expected total losses, how much should it charge for the policy? Round your answer to the nearest dollar

Answer 1

expected payout
E[x] = 30,000(0.01191 + 0.01292 + 0.01396 + 0.01503 + 0.01613)
= $2,098.50
=> $2,099
charge needed for $900 profit
= $(2099 + 900)
= $2999