You are given the following information about Bond A and Bond B:

1. Bond A is a 20-year bond that has 10,000 face amount, an annual coupon rate of 7% payable semiannually, and has a redemption value that is 10% higher than its price. Bond A is bought to yield an annual nominal interest rate of 5% convertible semiannually.
2. Bond B is an n-year bond with semiannual coupons and the same face amount, redemption value, coupon rate, and yield rate as Bond A. The price of Bond B is 158.33 less than the price of Bond A.

Calculate n

• 12
• 17
• 24
• 36
• 48

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

Solution: C

[[math]]\begin{aligned} & P_A=350 a_{\overline{400} | 0.025}+1.1 P_A v^{40} \\ & P_A=8785.97+P_A(0.409674) \\ & P_A=14,883.24 \\ & R=1.1 P_A=16,371.57 \\ & 14,724.91=350 a_{\overline{m} |0.025}+16,371.57 v^m \\ & m=48 \\ & n=24\end{aligned}[[/math]]

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