Revision as of 21:14, 19 November 2023 by Admin (Created page with "A zero-coupon bond with a face value of 1000 sells for a price of 600 and matures in n years, where n is a whole number. A second bond has the same price, same time until maturity, and same annual effective yield. It pays annual coupons at an annual rate equal to 50% of the annual effective yield rate. Calculate the face value of the second bond. <ul class="mw-excansopts"><li>666.67</li><li>750.00</li><li>774.60</li><li>800.00</li><li>826.40</li></ul> {{soacopyright |...")
ABy Admin
Nov 19'23
Exercise
A zero-coupon bond with a face value of 1000 sells for a price of 600 and matures in n years, where n is a whole number. A second bond has the same price, same time until maturity, and same annual effective yield. It pays annual coupons at an annual rate equal to 50% of the annual effective yield rate.
Calculate the face value of the second bond.
- 666.67
- 750.00
- 774.60
- 800.00
- 826.40
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: B
[[math]]\begin{aligned} & 600(1+i)^n=1000 \\ & (1+i)^n=\frac{10}{6} \\ & v^n=0.6 \\ & 600=F \frac{i}{2} a_{\overline{n}|i}+F v^n \\ & 600=F\left[\frac{i}{2} \frac{1-v^n}{i}+v^n\right] \\ & 600=F\left[\frac{1}{2}(1-0.6)+0.6\right] \\ & F=750\end{aligned}[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.