Revision as of 11:43, 20 November 2023 by Admin (Created page with "'''Solution: C''' If the bond has no premium or discount, it was bought at par so the yield rate equals the coupon rate, 0.038. <math display = "block"> \begin{align*} d &= \frac{\frac{1}{2}\biggl(1(190)v+2(190)v^{2}+\cdots+14(190)v^{14}+14(5000)v^{14}\biggr)}{190v+190v^{2}+\cdots+190v^{14}+5000v^{14}} \\ d &= \frac{95\bigl(Ia\bigr)_{\overline{{{14}}}|}+7\bigl(5000\bigr)v^{14}}{190a_{\overline{14}|}+5000v^{14}}\\ d = 5.5554 \end{align*} </math> Or, taking advantage o...")
Exercise
Nov 20'23
Answer
Solution: C
If the bond has no premium or discount, it was bought at par so the yield rate equals the coupon rate, 0.038.
[[math]]
\begin{align*}
d &= \frac{\frac{1}{2}\biggl(1(190)v+2(190)v^{2}+\cdots+14(190)v^{14}+14(5000)v^{14}\biggr)}{190v+190v^{2}+\cdots+190v^{14}+5000v^{14}} \\
d &= \frac{95\bigl(Ia\bigr)_{\overline{{{14}}}|}+7\bigl(5000\bigr)v^{14}}{190a_{\overline{14}|}+5000v^{14}}\\
d = 5.5554
\end{align*}
[[/math]]
Or, taking advantage of a shortcut:
[[math]]d=\ddot{a}_{\overline{14}|0.038}=11.1107[[/math]]
This is in half years, so dividing by two [math]d = 11.1107/2 = 5.5554[/math].
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.