Let A and B be bonds with semiannual coupons as described in the table below:

Bond	Price	Annual coupon rate	Par	Years to redemption	Annual nominal yield rate convertible semiannually
A	X	8%	1000	5	6%
B	X	y	1000	5	7%

Calculate y.

• 8.45%
• 8.65%
• 8.85%
• 9.05%
• 9.25%

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: D

Let C be the amount of the semiannual coupon for bond B.

[[math]] \begin{array}{l}{{{ X}=40a_{\overline{100}|0.03}+1000(1.03)^{-10}=1085.30}}\\ {{{ X}=1085.30=C a_{\bar{1}00.035}+1000(1.035)^{-10}=8.3166C+708.9188}}\\ {{{ C}=(1085.30-708.9188)/8.3166=45.2566}}\\ {{{ Y}=\frac{45.25660 \times 2}{1000}=.0905=9.059 \%}}\end{array} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.