Bond A and Bond B are each five-year 1000 face amount bonds. In addition:

1. Bond A has an annual coupon rate of 5% paid semiannually.
2. Bond B has an annual coupon rate of 3% paid annually.
3. The price of Bond B is 100 less than the price of Bond A.
4. The annual effective yield rate for Bond A is 4%.

Calculate the annual effective yield rate for Bond B.

• 4.15%
• 4.20%
• 4.25%
• 4.30%
• 4.35%

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

Solution: B

Using the BA II Plus calculator:

[[math]] \begin{aligned} & 1.04=\left(1+\frac{i^{(2)}}{2}\right)^2 \\ & \frac{i^{(2)}}{2}=0.019804 \\ & P_A=25 a_{\overline{100}|.019804}+1000 v^{10} \\ & P_A=1046.72 \\ & 1046.72-100=30 a_{\overline{5} \mid j}+1000 v_j^5 \\ & j=4.2036 \% \end{aligned} [[/math]]

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