An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The amount of the benefit decreases by 1000 each successive year until it reaches 0. If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.4.

Calculate the expected benefit under this policy.

• 2234
• 2400
• 2500
• 2667
• 2694

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

Solution: E

E[Y] = 4000(0.4) + 3000(0.6)(0.4) + 2000(0.6) 2 (0.4) + 1000(0.6)3 (0.4) = 2694.

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