Consider two 30-year bonds with the same purchase price. Each has an annual coupon rate of 5% paid semiannually and a par value of 1000. The first bond has an annual nominal yield rate of 5% compounded semiannually, and a redemption value of 1200. The second bond has an annual nominal yield rate of j compounded semiannually, and a redemption value of 800.

Calculate j.

• 2.20%
• 2.34%
• 3.53%
• 4.40%
• 4.69%

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

Solution: D

The price of the first bond is

[[math]] 1000(0.05/\,2)a_{\overline{30 \times 2}|0.05/2}+1200(1+0.05/\,2)^{-50\times2}=25a_{\overline{60}|0.025}+1200(1.025)^{-60} = 772.72 + 272.74 = 1, 045.46. [[/math]]

The price of the second bond is also 1,045.46. The equation to solve is

[[math]] 1,045.46=25a_{{\overline{{60}}}|j/2}+800(1+j\ /2)^{-60} [[/math]]

The financial calculator can be used to solve for j/2 = 2.2% for j = 4.4%.

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