Revision as of 23:00, 26 November 2023 by Admin (Created page with "'''Solution: C''' At time 5, the value of the perpetuity and annuity must be equal so <math display="block"> \begin{gathered} 100 a_{\overline{\infty} \mid}=X v+X(1.08) v^2+\cdots+X(1.08)^{24} v^{25} \text { or } \\ 100 / i=25 X v . \end{gathered} </math> At time 15, the remaining value of the annuity must equal the value of the perpetuity of <math>Y</math>. Thus <math display="block"> \begin{gathered} X(1.08)^{10} v+X(1.08)^{11} v^2+\cdots+X(1.08)^{24} v^{15}=Y a_...")
Exercise
Nov 26'23
Answer
Solution: C
At time 5, the value of the perpetuity and annuity must be equal so
[[math]]
\begin{gathered}
100 a_{\overline{\infty} \mid}=X v+X(1.08) v^2+\cdots+X(1.08)^{24} v^{25} \text { or } \\
100 / i=25 X v .
\end{gathered}
[[/math]]
At time 15, the remaining value of the annuity must equal the value of the perpetuity of [math]Y[/math]. Thus
[[math]]
\begin{gathered}
X(1.08)^{10} v+X(1.08)^{11} v^2+\cdots+X(1.08)^{24} v^{15}=Y a_{\overline{\infty}} \\
15 X v(1.08)^{10}=Y / i .
\end{gathered}
[[/math]]
Thus [math]Y=\frac{15}{25}(1.08)^{10}=129.5355[/math].
References
Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.