Revision as of 21:10, 19 November 2023 by Admin (Created page with " A 27-year bond, with a price equal to 75% of its face value, offers annual coupons with the coupon rate equal to 21/37 of the annual effective yield rate. An n-year zero-coupon bond has the same price, face value, and yield rate. Calculate n. <ul class="mw-excansopts"><li>5</li><li>7</li><li>9</li><li>11</li><li>13</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
A 27-year bond, with a price equal to 75% of its face value, offers annual coupons with the coupon rate equal to 21/37 of the annual effective yield rate. An n-year zero-coupon bond has the same price, face value, and yield rate.
Calculate n.
- 5
- 7
- 9
- 11
- 13
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: C
[[math]]
\begin{aligned} & 0.75 F=\frac{21}{37} i F a_{\overline{27}|i}+F v^{27} \\ & 0.75=\frac{21}{37}\left(1-v^{27}\right)+v^{27} \\ & 0.18243=\frac{16}{37} v^{27} \\ & i=0.03248 \\ & 0.75 F=F v^n \\ & (1+i)^n=\frac{4}{3} \\ & n=9\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.