Bond A is a 15-year 1000 face amount bond with an annual coupon rate of 9% paid semiannually. Bond A will be redeemed at 1200 and is bought to yield 8.4% convertible semiannually. Bond B is an n-year 1000 face amount bond with an annual coupon rate of 8% paid quarterly. Bond B will be redeemed at 1376.69 and is bought to yield 8.4% convertible quarterly. The two bonds have the same purchase price.

Calculate n.

• 12
• 14
• 15
• 16
• 18

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

Solution: A

[[math]] \begin{aligned} & P_A=45 a_{\overline{30} \mid 0.04}+1200 v^{30} \\ & P_A=1108.85 \\ & 1108.85=20 a_{\overline{4n}|0.021}+1376.69 v^{4n} \end{aligned} [[/math]]

Using the BA II Plus:

[[math]] \begin{aligned} & \mathrm{PV}=1108.85 \\ & \mathrm{PMT}=20 \\ & \mathrm{FV}=1376.69 \\ & \mathrm{I} / \mathrm{Y}=2.1 \end{aligned} [[/math]]

Solve for [math]4 n[/math] and get [math]4 n=48, n=12[/math]. Or solve the equation to get [math]v^{4 n}=0.36876[/math] and then solve for [math]n[/math].

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