An investor pays 962.92 for a ten-year bond with an annual coupon rate of 8% paid semiannually. The annual nominal yield rate is 10% convertible semiannually.

Calculate the discount of this purchase.

• 117
• 122
• 127
• 132
• 137

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

Solution: E

[[math]] \begin{array}{l}{{P=C+(F r-C i)a_{\overline{n}|}}}\\ {{962.92=C+(0.04C-0.05C)a_{\overline{20} |0.05}}}\\ {{962.92=C+(-0.01C)12.46221}}\\ {{C=1100}}\end{array} [[/math]]

The discount is 1100 – 962.92 = 137.08

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