Revision as of 21:15, 19 November 2023 by Admin (Created page with " A zero-coupon bond with a face amount of 1000 sells for a price of 640 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>780</li><li>805</li><li>830</li><li>855</li><li>880</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
A zero-coupon bond with a face amount of 1000 sells for a price of 640 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.
- 780
- 805
- 830
- 855
- 880
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: A
[[math]]
\begin{aligned} & 640(1+i)^n=1000 \\ & (1+i)^n=1.5625 \\ & v^n=0.64 \\ & 640=F \frac{i}{2} a_{\overline{n} i}+F v^n \\ & 640=F\left[\frac{i}{2} \frac{1-v^n}{i}+v^n\right] \\ & 640=F\left[\frac{1}{2}(1-0.64)+0.64\right] \\ & F=780.49\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.