The annualized yield on a three-year security is 13 percent; the annualized two-year interest rate is 12 percent, while the one-year interest rate is 9 percent. The forward rate one year ahead is ____ percent.
A)2.8
B)115
C)103
D)15.1

Question

Quizplus · Accepted Answer

The forward rate can be calculated using the formula that equates the return from investing in a long-term bond to the return from rolling over short-term bonds. Given a three-year bond at 13% annualized yield, a two-year bond at 12%, and a one-year bond at 9%, we can calculate the one-year forward rate one year from now as follows:Let $F$ be the forward rate we are looking for. The idea is to make the investment outcomes equivalent whether we invest for three years directly or invest for one year and then invest the proceeds for two more years at the forward rate.Investing in the three-year security at 13% for three years gives us a return factor of $(1 + 0.13)^3$.Investing in the one-year security at 9% for one year and then investing the proceeds for two more years at the forward rate $F$ gives us a return factor of $(1 + 0.09) \times (1 + F)^2$.Setting these equal to each other:$$(1 + 0.13)^3 = (1 + 0.09) \times (1 + F)^2$$Solving for $F$ gives us the forward rate. Without going through the algebraic steps here (since the calculation detail was not requested), following the correct procedure will lead you to find that $F$ is approximately 15.1%, which corresponds to choice D.

The Annualized Yield on a Three-Year Security Is 13 Percent;