Revision as of 13:55, 20 November 2023 by Admin (Created page with "'''Solution: C''' Let <math>i</math> be the yield rate. Then, <math display = "block"> \begin{aligned} & 3609.29=2000(2 i) a_{\overline{30}|i}+2250(1+i)^{-30} \\ & =4000\left[1-(1+i)^{-30}\right]+2250(1+i)^{-30} \\ & (1+i)^{-30}=(4000-3609.29) /(4000-2250)=0.22326 \\ & i=0.22326^{-1 / 30}-1=0.051251 . \end{aligned} </math> Modified duration is Macaulay duration divided by one plus the yield rate: <math>14.14 / 1.051251=</math> 13.71. {{soacopyright | 2023 }}")
Exercise
Nov 20'23
Answer
Solution: C
Let [math]i[/math] be the yield rate. Then,
[[math]]
\begin{aligned}
& 3609.29=2000(2 i) a_{\overline{30}|i}+2250(1+i)^{-30} \\
& =4000\left[1-(1+i)^{-30}\right]+2250(1+i)^{-30} \\
& (1+i)^{-30}=(4000-3609.29) /(4000-2250)=0.22326 \\
& i=0.22326^{-1 / 30}-1=0.051251 .
\end{aligned}
[[/math]]
Modified duration is Macaulay duration divided by one plus the yield rate: [math]14.14 / 1.051251=[/math] 13.71.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.