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 two years ahead is ____ percent.
A)1.8
B)9.0
C)15.0
D)none of the above

Question

Quizplus · Accepted Answer

To calculate the forward rate, we can use the formula:

(1 + r3)^3 = (1 + r1)^1 x (1 + f2)^2

Where r3 is the three-year interest rate, r1 is the one-year interest rate, and f2 is the forward rate two years ahead.

Plugging in the given values, we get:

(1 + 0.13)^3 = (1 + 0.09)^1 x (1 + f2)^2
1.4641 = 1.09 x (1 + f2)^2
(1 + f2)^2 = 1.4641/1.09
1 + f2 = (1.4641/1.09)^(1/2)
f2 = (1.4641/1.09)^(1/2) - 1
f2 = 0.1507 or 15.07%

Therefore, the forward rate two years ahead is 15.07%. The correct answer is (C).

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