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.

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.