An insurance company sells a policy with a linearly disappearing deductible such that no payment is made on a claim of 250 or less and full payment is made on a claim of 1000 or more.

Calculate the payment made by the insurance company for a loss of 700.

• 450
• 500
• 550
• 600
• 700

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

Key: D

At 250 the payment is 0. At 1000 the payment is 1000. Interpolating:

[[math]] \frac{700-250}{1000-250} = \frac{x-0}{1000-0} \Rightarrow x = 450(1000)750 = 600. [[/math]]

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