excans:B8d33a4aef: Difference between revisions
From Stochiki
No edit summary |
No edit summary |
||
| Line 18: | Line 18: | ||
<math display = "block">1000_{2 \mid 3} q_{[60]+0.75}=116.8</math> | <math display = "block">1000_{2 \mid 3} q_{[60]+0.75}=116.8</math> | ||
{{soacopyright|2024}} | |||
{{soacopyright|2024}} | {{soacopyright|2024}} | ||
Revision as of 02:34, 18 January 2024
Answer: B
Under constant force over each year of age, [math]l_{x+k}=\left(l_{x}\right)^{1-k}\left(l_{x+1}\right)^{k}[/math] for [math]x[/math] an integer and [math]0 \leq k \leq 1[/math].
[[math]]
\begin{aligned}
& { }_{2 \mid 3} q_{[60]+0.75}=\frac{l_{[60]+2.75}-l_{[60]+5.75}}{l_{[60]+0.75}} \\
& l_{[60]+0.75}=(80,000)^{0.25}(79,000)^{0.75}=79,249 \\
& l_{[60]+2.75}=(77,000)^{0.25}(74,000)^{0.75}=74,739 \\
& l_{[60]+5.75}=(67,000)^{0.25}(65,000)^{0.75}=65,494
\end{aligned}
[[/math]]
[[math]]{ }_{2 \mid 3} q_{[60]+0.75}=\frac{l_{[60]+2.75}-l_{[60]+5.75}}{l_{[60]+0.75}}=\frac{74,739-65,494}{79,249}=0.11679[[/math]]
[[math]]1000_{2 \mid 3} q_{[60]+0.75}=116.8[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.