Revision as of 19:21, 19 November 2023 by Admin (Created page with "'''Solution: E''' The bond sells at a premium, so the worst-case scenario is redemption at time six. Then, <math display = "block"> \begin{array}{l}{{1023=1000\frac{i}{0.96}a_{\overline{{{6}}}|i}+1000(1+i)^{-6}}}\\ {{=\frac{1000}{0.96}[1-(1+i)^{-6}]+1000(1+i)^{-6}}}\\ {{(1+i)^{-6}=0.448}}\\ {{\dot{\displaystyle i=0.448^{-1/6}-1=0.1432}}}\\ i=14.32\% \end{array} </math> {{soacopyright | 2023 }}")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: E
The bond sells at a premium, so the worst-case scenario is redemption at time six. Then,
[[math]]
\begin{array}{l}{{1023=1000\frac{i}{0.96}a_{\overline{{{6}}}|i}+1000(1+i)^{-6}}}\\ {{=\frac{1000}{0.96}[1-(1+i)^{-6}]+1000(1+i)^{-6}}}\\
{{(1+i)^{-6}=0.448}}\\ {{\dot{\displaystyle i=0.448^{-1/6}-1=0.1432}}}\\
i=14.32\%
\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.