If the current 3-year interest rate is 2.6% and the expected 1-year interest rate three years from now is 1.0%, what is the interest rate on 4-year bond today according to the expectations theory?
a. 4.4 percent.
b. 1.1 percent.
c. 2.2 percent.
d. 2.0 percent.
Expectation theory tells us that:
In = (i0 + i1 + ------+ in-1)/n
where In = interest rate on 4-year bond today and in = expected 1-year interest rate n years from now.
Using above data we have :
Now we have I3 =2.6% and I3 = (i0 + i1 + i2)/3 => (i0 + i1 + i2) = 3*2.6 = 7.8%
So, I4 = (7.8 + i3)/4
It is given that expected 1-year interest rate three years from now is 1.0% => i3 = 1%
So, I4 = (7.8 + 1)/4 = 2.2%
Thus, current 4-year Bond interest rate = 2.2%
Hence, the correct answer is (c) 2.2 percent.
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