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.

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.