Revision as of 18:57, 19 November 2023 by Admin (Created page with "Bond A and Bond B are both annual coupon, five-year, 10,000 par value bonds bought to yield an annual effective rate of 4%. <ul style="list-style-type:lower-roman"> <li>Bond A has an annual coupon rate of r%, a redemption value that is 10% below par, and a price of P.</li> <li>Bond B has an annual coupon rate of (r+1)%, a redemption value that is 10% above par, and a price of 1.2P</li> </ul> Calculate r %. <ul class="mw-excansopts"><li>5.85%</li><li>6.85%</li><li>7.8...")
ABy Admin
Nov 19'23
Exercise
Bond A and Bond B are both annual coupon, five-year, 10,000 par value bonds bought to yield an annual effective rate of 4%.
- Bond A has an annual coupon rate of r%, a redemption value that is 10% below par, and a price of P.
- Bond B has an annual coupon rate of (r+1)%, a redemption value that is 10% above par, and a price of 1.2P
Calculate r %.
- 5.85%
- 6.85%
- 7.85%
- 8.85%
- 9.85%
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: B
The two equations are:
[[math]]
\begin{array}{l}{{P=(10,000r)a_{\overline{50}|0.04}+9,000(1.04)^{-5}=44,518.22r+7,397.34}}\\ {{1.2P=[10,000(r+0.01)]a_{\overline{50}|0.04}+11,000(1.04)^{-5}=44,518.22r+9,486.38}}\end{array}
[[/math]]
Subtracting the first equation from the second gives 0.2P = 2089.04 for P = 10,445.20. Inserting this in the first equation gives r = (10,445.20 – 7,397.34)/44,518.22 = 0.0685.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.