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(Created page with "'''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 display="block"> \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)^{...") |
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<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 display = "block">{ }_{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> | <math display = "block">1000_{2 \mid 3} q_{[60]+0.75}=116.8</math> | ||
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Latest 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.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.