Revision as of 21:31, 19 November 2023 by Admin (Created page with "A three-year 1000 face amount bond pays coupons of X quarterly. It is bought at a price to yield an annual nominal rate of 8% convertible quarterly. If the amount of each coupon were doubled, the purchase price would have to increase by 500 for the bond to maintain the same yield rate. Calculate X. <ul class="mw-excansopts"><li>20</li><li>24</li><li>31</li><li>40</li><li>47</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
A three-year 1000 face amount bond pays coupons of X quarterly. It is bought at a price to yield an annual nominal rate of 8% convertible quarterly. If the amount of each coupon were doubled, the purchase price would have to increase by 500 for the bond to maintain the same yield rate.
Calculate X.
- 20
- 24
- 31
- 40
- 47
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: E
[[math]]
\begin{aligned}
& P=X a_{\overline{12} | 0.02}+1000 v^{12} \\
& 500+P=2 X a_{\overline{12} | 0.02}+1000 v^{12}
\end{aligned}
[[/math]]
Subtract the first equation from the second.
[[math]]
\begin{aligned}
& 500=X a_{\overline{12} \mid 0.02} \\
& X=47.28
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.