1. The igniter switch may need to be replaced at a cost of 60. There is a 0.10 probability of this.
2. The pilot light may need to be replaced at a cost of 200. There is a 0.05 probability of this.
3. The furnace may need to be replaced at a cost of 3000. There is a 0.01 probability of this.

Calculate the deductible that would produce an expected claim payment of 30

• 100
• At least 100 but less than 150
• At least 150 but less than 200
• At least 200 but less than 250
• At least 250

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

Solution: C

If the deductible is less than 60 the equation is, 0.10(60 − d ) + 0.05(200 − d ) + 0.01(3000 − d ) = 30 ⇒ d = 100. So this cannot be the answer. If the deductible is between 60 and 200, the equation is 0.05(200 − d ) + 0.01(3000 − d ) = 30 ⇒ d = 166.67 . This is consistent with the assumption and is the answer.

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