You are given the survival function:

[[math]]S_{0}(x)=\left(1-\frac{x}{60}\right)^{\frac{1}{3}}, \quad 0 \leq x \leq 60.[[/math]]

Calculate [math]1000 \mu_{35}[/math].

• 5.6
• 6.7
• 13.3
• 16.7
• 20.1

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

Answer: C

[[math]] \begin{aligned} \mu_{x} & =-\frac{d}{d_{x}} \ln S_{0}(x)=-\frac{1}{3} \frac{d}{d_{x}} \ln \left(1-\frac{x}{60}\right) \\ & =\frac{1}{180}\left(1-\frac{x}{60}\right)^{-1}=\frac{1}{3(60-x)} \end{aligned} [[/math]]

Therefore, [math]1000 \mu_{35}=(1000) \frac{1}{3(25)}=\frac{1000}{75}=13.3[/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.