You are given the following survival function:

[[math]] S_{0}(x)=\left(1-\frac{x}{100}\right)^{0.5}, 0 \leq x \leq 100 [[/math]]

Calculate [math]1000 \mu_{25}[/math].

• 6.7
• 10.0
• 13.3
• 16.7
• 20.0

Copyright 2024 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Answer: A

[math]\mu_{25}=\frac{-s^{\prime}(25)}{s(25)}=\frac{0.5(0.01)(1-0.01 \times 25)^{-0.5}}{(1-0.01 \times 25)^{0.5}}=0.00667[/math]

Copyright 2024 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.