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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>. | ||
{{soacopyright|2024}} | |||
{{soacopyright|2024}} | {{soacopyright|2024}} | ||
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.