What is the one-year interest rate one year from now if the current one-year interest rate is 2.75% and the two-year interest rate is 3.21%? Assume the rates are effective annual rates.
A)3.62%
B)3.67%
C)3.71%
D)3.75%
E)3.88%

Question

Quizplus · Accepted Answer

To find the one-year interest rate one year from now, we can use the concept of forward rates, which are implied by current spot rates (the given one-year and two-year interest rates). The formula to calculate the forward rate for the second year, given the spot rates for the first and second years, is:$$ (1 + r_2)^2 = (1 + r_1) \times (1 + f) $$where $ r_2 $ is the two-year spot rate (3.21%), $ r_1 $ is the one-year spot rate (2.75%), and $ f $ is the forward rate for the second year, which we are trying to find.Rearranging the formula to solve for $ f $:$$ f = \frac{(1 + r_2)^2}{(1 + r_1)} - 1 $$Plugging in the given rates:$$ f = \frac{(1 + 0.0321)^2}{(1 + 0.0275)} - 1 $$$$ f = \frac{(1.0321)^2}{1.0275} - 1 $$$$ f = \frac{1.0651}{1.0275} - 1 $$$$ f = 1.0366 - 1 $$$$ f = 0.0366 $$ or 3.66%, which when rounded to the nearest hundredth is 3.67%.

What Is the One-Year Interest Rate One Year from Now