Revision as of 01:24, 20 November 2023 by Admin (Created page with "Two bonds have the same annual effective yield rate, r, where r > 0. The bonds have Macaulay duration of 5 years and 6 years with respect to r. One of the bonds has modified duration of 5.76 years while the other bond has modified duration of d years. Calculate d. <ul class="mw-excansopts"><li>4.760</li><li>4.800</li><li>5.208</li><li>5.240</li><li>6.912</li></ul> {{soacopyright | 2023 }}")
Nov 20'23
Exercise
Two bonds have the same annual effective yield rate, r, where r > 0. The bonds have Macaulay duration of 5 years and 6 years with respect to r. One of the bonds has modified duration of 5.76 years while the other bond has modified duration of d years.
Calculate d.
- 4.760
- 4.800
- 5.208
- 5.240
- 6.912
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 20'23
Solution: B
[[math]]
\begin{aligned}
& \bar{v}=\frac{\bar{d}}{1+r} \\
& 5.76=\frac{6}{1+r} \\
& r=0.041667 \\
& \bar{v}=\frac{5}{1.041666}=4.8
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.