You are given the following:

(i) [math] e_{40:20}=18[/math]

(ii) [math]e_{60}=25[/math]

(iii) [math]{ }_{20} q_{40}=0.2[/math]

(iv) [math]q_{40}=0.003[/math]

Calculate [math]e_{41}[/math].

• 36.1
• 37.1
• 38.1
• 39.1
• 40.1

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

Answer: B

[[math]] \begin{aligned} & e_{40}=e_{40: 20}+{ }_{20} p_{40} \cdot e_{60} \\ & =18+(1-0.2)(25) \\ & =38 \\ & e_{40}=e_{40: 11}+p_{40} \cdot e_{41} \\ & \Rightarrow e_{41}=\frac{e_{40}-e_{40: 11}}{p_{40}}=\frac{e_{40}-p_{40}}{p_{40}}=\frac{38-0.997}{0.997}=37.11434 \end{aligned} [[/math]]

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