A bank issues two 20-year bonds, A and B, each with annual coupons, an annual effective yield rate of 10%, and a face amount of 1000. The total combined price of these two bonds is 1600. Bond B's annual coupon rate is equal to Bond A's annual coupon rate plus 1 percentage point.

Calculate the annual coupon rate of Bond A

• 6.46%
• 7.15%
• 7.29%
• 8.02%
• 8.90%

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

Solution: B

Let r be the coupon rate for Bond A. The coupon rate for Bond B is then r + 0.01. Then,

[[math]] \begin{align*} 1600=1000\left[\frac{1}{(1.1)^{20}}+r a_{\overline{{{20}}}|0.1}+\frac{1}{(1.1)^{20}}+(r+0.01)a_{\overline{{{20}}}|0.1}^{}\right] \\ 1.6=\frac{2}{(1.1)^{20}}+2r a_{\overline{{{20}}}|0.1}+0.01a_{\overline{{{20}}}|0.1}+0.01a_{\overline{{{20}}}|0.1}=0.29729+17.02713r+0.08514 \\ r=\frac{1.6-0.29729-0.08514}{17.02713}=0.0715=7.15\%. \end{align*} [[/math]]

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