An investor purchases a 20-year, 1000 face amount bond with semiannual coupons at a price equal to the redemption value of 900. The bond yields an annual nominal rate of 10% convertible semiannually. After ten years, the investor sells the bond, yielding to the buyer an annual nominal rate of 8% convertible semiannually. The investor uses the proceeds to purchase a 10-year, 1000 face amount bond with redemption value 1100 and semiannual coupons. The yield rate on the new bond is an annual nominal rate of 8% convertible semiannually.

Calculate the semiannual coupon payment for the new bond.

• 34
• 38
• 41
• 45
• 50

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

Solution: B

[[math]] 900=1000 r a_{\overline{40} \mid 0.05}+900 v^{40} [[/math]]

Using BA II Plus:

[[math]] \begin{aligned} & 1000 r=45 \\ & P=45 a_{\overline{20} \mid 0.04}+900 v^{20} \\ & P=1022.31 \\ & 1022.31=F r a_{\overline{20} \mid 0.04}+1100 v^{20} \\ & F r=38.28 \end{aligned} [[/math]]

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