Revision as of 19:17, 19 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>911</li><li>923</li><li>956</li><li>974</li><li>984</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
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.
ABy Admin
Nov 19'23
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.