A steel company issued a ten-year 1,000,000 face amount bond on March 1, 2002 with an annual nominal coupon rate of 8% paid semiannually. On September 2, 2004, Company X paid 1,100,000 for this bond to yield an annual nominal rate of i convertible semiannually.

Calculate i.

• 4.0%
• 5.5%
• 6.3%
• 8.0%
• 9.7%

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

Solution: C

[[math]] \begin{aligned} & M V_5=1,100,000=1,000,000 v^{15}+40,000 a_{\overline{15}| i^{(2)} / 2} \\ & \frac{i^{(2)}}{2}=.03153 \\ & i^{(2)}=0.06306\end{aligned} [[/math]]

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