A bond with a face value of 1000 and a redemption value of 1080 has an annual coupon rate of 8% payable semiannually. The bond is bought to yield an annual nominal rate of 10% convertible semiannually. At this yield rate, the present value of the redemption value is 601 on the purchase date.

Calculate the purchase price of the bond.

• 911
• 923
• 956
• 974
• 984

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

Solution: C

Let [math]n[/math] be the term of the bond in half-years. We know that [math]601=1080 v^n[/math] and thus [math]v^n=601 / 1080[/math] . Then

[[math]]a_{\overline{n} |0.05}=\frac{1-v^n}{0.05}=\frac{1-601 / 1080}{0.05}=8.87037[[/math]]

. The purchase price of the bond is

[[math]]40 a_{\overline{n}| 0.05}+1080 v^n=40(8.87037)+610=956.[[/math]]

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