Revision as of 18:52, 19 November 2023 by Admin (Created page with "You have decided to invest in Bond X, an n-year bond with semi-annual coupons and the following characteristics: *Par value is 1000. *The ratio of the semi-annual coupon rate, r, to the desired semi-annual yield rate, i, is 1.03125. *The present value of the redemption value is 381.50. Given <math>(1+i)^{-n} = 0.5889</math>, calculate the price of bond X. <ul class="mw-excansopts"><li>1019</li><li>1029</li><li>1050</li><li>1055</li><li>1072</li></ul> {{soacopyright |...")
Nov 19'23
Exercise
You have decided to invest in Bond X, an n-year bond with semi-annual coupons and the following characteristics:
- Par value is 1000.
- The ratio of the semi-annual coupon rate, r, to the desired semi-annual yield rate, i, is 1.03125.
- The present value of the redemption value is 381.50.
Given [math](1+i)^{-n} = 0.5889[/math], calculate the price of bond X.
- 1019
- 1029
- 1050
- 1055
- 1072
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 19'23
Solution: D
Let C be the redemption value and [math]v = 1/(1+i)[/math]. Then
[[math]]
\begin{align*} X &= 1000r a_{\overline{2n}|i}+C\nu^{2n}\\ &=1000r\frac{1-\nu^{2n}}{i}+381.50\\ &=10000(1.03125)(1-0.5889^{2})+381.50 \\
&=1055.11
\end{align*}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.