An auto insurance company is implementing a new bonus system. In each month, if a policyholder does not have an accident, he or she will receive a cash-back bonus of 5 from the insurer. Among the 1,000 policyholders of the auto insurance company, 400 are classified as low-risk drivers and 600 are classified as high-risk drivers. In each month, the probability of zero accidents for high-risk drivers is 0.80 and the probability of zero accidents for low-risk drivers is 0.90. Calculate the expected bonus payment from the insurer to the 1000 policyholders in one year.

• 48,000
• 50,400
• 51,000
• 54,000
• 60,000

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

The expected bonus for a high-risk driver is 0.8(12)(5) = 48.

The expected bonus for a low-risk driver is 0.9(12)(5) = 54.

The expected bonus payment from the insurer is 600(48) + 400(54) = 50,400.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.