You are given the following information about a 20-year bond with face amount 1000:

• The bond has an annual coupon rate of r payable semiannually and is redeemable at par.
• The nominal annual yield rate convertible semiannually is 7.2%.
• The amount for accumulation of discount in the seventh coupon payment is 4.36.

Calculate r.

• 2.1%
• 4.0%
• 4.3%
• 6.0%
• 6.9%

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C

The book value after the sixth coupon is

[[math]] 1000(r/2)a_{\overline{{{34}}}|0.036}+1000(1.036)^{-34}=9716.01r+300.45 [[/math]]

After the seventh coupon it is

[[math]] 1000(r/2)a_{\overline{{{33}}}|0.036}+1000(1.036)^{-33}=9565.79r+311.26 [[/math]]

Then,

[[math]] \begin{array}{l}{{4.36=9565.79r+311.26-(9716.01r+300.45)=10.81-150.22r}}\\ {{r=(10.81-4.36)/150.22=0.0429.}}\end{array} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.