Revision as of 19:20, 19 November 2023 by Admin (Created page with "A ten-year 1000 par value bond with coupons paid annually at an annual rate of r is callable at par at the end of the 6th , 7th , 8th , or 9th year. The price of the bond is 1023. If the bond is called in the worst-case scenario for the bond investor, the resulting annual effective yield rate, i, is 96% of r. Calculate i. <ul class="mw-excansopts"><li>4.41%</li><li>7.46%</li><li>8.36%</li><li>10.56%</li><li>14.32%</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
A ten-year 1000 par value bond with coupons paid annually at an annual rate of r is callable at par at the end of the 6th , 7th , 8th , or 9th year. The price of the bond is 1023. If the bond is called in the worst-case scenario for the bond investor, the resulting annual effective yield rate, i, is 96% of r.
Calculate i.
- 4.41%
- 7.46%
- 8.36%
- 10.56%
- 14.32%
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
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.