Revision as of 20:59, 19 November 2023 by Admin (Created page with "A bank issues two 20-year par-value bonds providing annual coupons. Each bond sells for the same price and provides an annual effective yield rate of 6.5%. The first bond has a redemption value of 6000 and a coupon of 7.6% paid annually. The second bond has a redemption value of 7500 and a coupon of r% paid annually. Calculate r. <ul class="mw-excansopts"><li>5.6</li><li>5.9</li><li>6.1</li><li>6.7</li><li>7.2</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
A bank issues two 20-year par-value bonds providing annual coupons. Each bond sells for the same price and provides an annual effective yield rate of 6.5%. The first bond has a redemption value of 6000 and a coupon of 7.6% paid annually. The second bond has a redemption value of 7500 and a coupon of r% paid annually.
Calculate r.
- 5.6
- 5.9
- 6.1
- 6.7
- 7.2
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: A
For the first bond:
[[math]]
(0.076)(6000)a_{\overline{20}|0.065}+6000v^{20}, \, P = 6727.22.
[[/math]]
For the second bond:
[[math]]
6727.22=(r)(7500)a_{\overline{{{20}}}\mid0.065}+7500v^{20}, \, 7500r = 417.37, \implies r = 0.0556.
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.