A ten-year bond paying annual coupons of X has a face amount of 1000, a price of 450, and an annual effective yield rate of 10%. A second ten-year bond has the same face amount and annual effective yield rate as the first bond. This second bond pays semi-annual coupons of X/2. The price of the second bond is P.

Calculate P.

• 439
• 442
• 452
• 457
• 461

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

Solution: C

[[math]] 450 = X a_{\overline{10}|0.10} + 1000v^{10} \\ [[/math]]

Using BA II Plus calculator:

[[math]] \begin{aligned} X = 10.50 \\ 1.10 = (1+j)^2, \, j = 0.048881 \\ P = 5.25 a_{\overline{20}|0.048881} + 1000v^{20} \\ P = 451.64 \end{aligned} [[/math]]

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