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.

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.