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(Created page with "'''Answer: C''' We need to determine <math>{ }_{3 \mid 2.5} q_{90}</math>. <math display="block"> { }_{3 \mid 2.5} q_{90}=\frac{l_{90+3}-l_{90+3+2.5}}{l_{90}}=\frac{l_{93}-l_{95.5}}{l_{90}}=\frac{l_{93}-\left(l_{95}-0.5 d_{95}\right)}{l_{90}}=\frac{825-[600-0.5(240)]}{1,000}=0.3450 </math> where <math>l_{90}=1,000, l_{93}=825, l_{97}=\frac{d_{97}}{q_{97}}=\frac{72}{1}=72, l_{96}=\frac{l_{97}}{p_{96}}=\frac{72}{0.2}=360</math>, <math>l_{95}=\frac{l_{96}}{p_{95}}=\f...") |
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<math>l_{95}=\frac{l_{96}}{p_{95}}=\frac{360}{1-0.4}=600</math>, and <math>d_{95}=l_{95}-l_{96}=600-360=240</math>. | <math>l_{95}=\frac{l_{96}}{p_{95}}=\frac{360}{1-0.4}=600</math>, and <math>d_{95}=l_{95}-l_{96}=600-360=240</math>. | ||
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Latest revision as of 02:34, 18 January 2024
Answer: C
We need to determine [math]{ }_{3 \mid 2.5} q_{90}[/math].
[[math]]
{ }_{3 \mid 2.5} q_{90}=\frac{l_{90+3}-l_{90+3+2.5}}{l_{90}}=\frac{l_{93}-l_{95.5}}{l_{90}}=\frac{l_{93}-\left(l_{95}-0.5 d_{95}\right)}{l_{90}}=\frac{825-[600-0.5(240)]}{1,000}=0.3450
[[/math]]
where [math]l_{90}=1,000, l_{93}=825, l_{97}=\frac{d_{97}}{q_{97}}=\frac{72}{1}=72, l_{96}=\frac{l_{97}}{p_{96}}=\frac{72}{0.2}=360[/math],
[math]l_{95}=\frac{l_{96}}{p_{95}}=\frac{360}{1-0.4}=600[/math], and [math]d_{95}=l_{95}-l_{96}=600-360=240[/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.