A bank issues two 30-year bonds, A and B, each with annual coupons, an annual effective yield rate of 7%, and a face amount of 1000. The total price of these two bonds is 3000. Bond B's annual coupon rate is equal to Bond A's annual coupon rate plus 0.5%.

Calculate the annual coupon rate of Bond A.

• 10.06%
• 10.78%
• 10.90%
• 11.31%
• 11.84%

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

Solution: B

Let [math]r_A[/math] represent the coupon rate of bond [math]\mathrm{A}[/math]. The coupon rate of bond [math]\mathrm{B}[/math] is then [math]r_A+0.005[/math]. From the given information,

[[math]] \begin{aligned} & 3000=1000\left[\frac{1}{(1.07)^{30}}+r_A a_{\overline{30} \mid 0.07}+\frac{1}{(1.07)^{30}}+\left(r_A+0.005\right) a_{\overline{30} \mid 0.07}\right] \\ & 3=\frac{2}{(1.07)^{30}}+2 r_A a_{\overline{30} \mid 0.07}+0.005 a_{\overline{30} \mid 0.07} \\ & 3=0.26273+24.81808 r_A+0.06205 \\ & r_A=\frac{3-0.26273-0.06205}{24.81808}=0.1078=10.78 \% \end{aligned} [[/math]]

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