Revision as of 21:23, 19 January 2024 by Admin (Created page with "'''Answer: D''' <math>\operatorname{EPV}(</math> Premiums <math>)=\operatorname{EPV}(</math> Benefits <math>)</math> <math>\mathrm{EPV}(</math> Premiums <math>)=3 P \bar{a}_{x}-2 P_{20} E_{x} \bar{a}_{x+20}</math> <math display="block"> \begin{aligned} & =3 P(1 / \mu+\delta)-2 P\left(e^{-20(\mu+\delta)}\right)(1 / \mu+\delta) \\ & =3 P(1 / 0.09)-2 P e^{-1.8}-1 / 0.09 \\ & =29.66 P \end{aligned} </math> <math>\operatorname{EPV}(</math> Benefits <math>)=1,000,000 \b...")
Exercise
ABy Admin
Jan 19'24
Answer
Answer: D
[math]\operatorname{EPV}([/math] Premiums [math])=\operatorname{EPV}([/math] Benefits [math])[/math]
[math]\mathrm{EPV}([/math] Premiums [math])=3 P \bar{a}_{x}-2 P_{20} E_{x} \bar{a}_{x+20}[/math]
[[math]]
\begin{aligned}
& =3 P(1 / \mu+\delta)-2 P\left(e^{-20(\mu+\delta)}\right)(1 / \mu+\delta) \\
& =3 P(1 / 0.09)-2 P e^{-1.8}-1 / 0.09 \\
& =29.66 P
\end{aligned}
[[/math]]
[math]\operatorname{EPV}([/math] Benefits [math])=1,000,000 \bar{A}_{x}-500,000{ }_{20} E_{x} \bar{A}_{x+20}[/math]
[[math]]
\begin{aligned}
& =1,000,000(\mu / \mu+\delta)-500,000 e^{-20(\mu+\delta)} \mu / \mu+\delta \\
& =1,000,000(0.03 / 0.09)-500,000 e^{-1.8} 0.03 / 0.09 \\
& =305,783.5
\end{aligned}
[[/math]]
[math]29.66 P=305,783.5[/math]
[[math]]
P=\frac{305,783.5}{29.66}
[[/math]]
[[math]]
P=10,309.62
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.