Revision as of 08:52, 18 November 2023 by Admin (Created page with "'''Solution: D''' The present value of the perpetuity = X/i. Let B be the present value of Brian’s payments. <math display = "block"> \begin{align*} B=X a_{\overline{n}|i}=0.4{\frac{X}{i}} \\ K=0.36{\frac{X}{i}} \\ a_{\overline{n}|i}=\frac{0.4}{i}\Longrightarrow0.4=1-{\nu}^{n}\Longrightarrow{\nu}^{n}=0.6 \\ K=\nu^{2n}\,{\frac{X}{i}} \\ K = 0.36 \frac{X}{i} \end{align*} </math> Thus the charity’s share is 36% of the perpetuity’s present value. {{soacopyright | 2...")
Exercise
ABy Admin
Nov 18'23
Answer
Solution: D
The present value of the perpetuity = X/i. Let B be the present value of Brian’s payments.
[[math]]
\begin{align*}
B=X a_{\overline{n}|i}=0.4{\frac{X}{i}} \\
K=0.36{\frac{X}{i}} \\
a_{\overline{n}|i}=\frac{0.4}{i}\Longrightarrow0.4=1-{\nu}^{n}\Longrightarrow{\nu}^{n}=0.6 \\
K=\nu^{2n}\,{\frac{X}{i}} \\
K = 0.36 \frac{X}{i}
\end{align*}
[[/math]]
Thus the charity’s share is 36% of the perpetuity’s present value.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.