Revision as of 02:46, 16 January 2024 by Admin (Created page with "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>. <ul class="mw-excansopts"><li> 36.1</li><li> 37.1</li><li> 38.1</li><li> 39.1</li><li> 40.1</li></ul>")
Jan 16'24
Exercise
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
Jan 16'24
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.