An investor buys a one-year bond with a face amount of 100 and an annual coupon rate of 6% paid semiannually. The bond is purchased at a discount of 1.50 to yield an annual nominal rateof j convertible semiannually.

Calculate j.

• 0.022
• 0.038
• 0.068
• 0.076
• 0.136

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

Solution: D

[[math]]\begin{aligned} & 98.5=3 a_{2 j_{j / 2}}+100 v^2 \\ & \frac{j}{2}=0.037929 \\ & j=0.07586\end{aligned}[[/math]]

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