Revision as of 22:47, 17 November 2023 by Admin (Created page with "'''Solution: C''' <math display = "block"> \begin{align*} \ {\frac{\left(1-d/2\right)^{-4}}{\left(1-d/4\right)^{-4}}}=\left({\frac{39}{38}}\right)^{4}\Rightarrow{\frac{1-d/2}{1-d/4}}={\frac{38}{39}}\Rightarrow39-39(d/2)=38-38(d/4) \\ d(39/2 -38/4) = 39-38 \\ d = 1/(19.5-9.5)=0.1 \\ 1+i=\left(1-d/\,2\right)^{-2}=95^{-2}=1.108\Longrightarrow i=10.8 \% \end{align*} </math> {{soacopyright | 2023 }}")
Exercise
ABy Admin
Nov 17'23
Answer
Solution: C
[[math]]
\begin{align*}
\ {\frac{\left(1-d/2\right)^{-4}}{\left(1-d/4\right)^{-4}}}=\left({\frac{39}{38}}\right)^{4}\Rightarrow{\frac{1-d/2}{1-d/4}}={\frac{38}{39}}\Rightarrow39-39(d/2)=38-38(d/4) \\
d(39/2 -38/4) = 39-38 \\
d = 1/(19.5-9.5)=0.1 \\
1+i=\left(1-d/\,2\right)^{-2}=95^{-2}=1.108\Longrightarrow i=10.8 \%
\end{align*}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.