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.