From the following information, find (a) yield on 1-year T-bonds one year from now; (b) yield on 2-year T-bonds one year from now; and (c) yield on 1-year T-bonds two years from now?

As on date today, interest rates on 1-year T-bonds yield 1.7%, interest rates on 2-year T-bonds yield 2.15%, and interest rates on 3-year T-bonds yield 3.8%.

1 Answer
Dec 3, 2017

(a) 2.6% - (b) 4.866% - (c) 7.18%

Explanation:

We are given that today, interest rates on 1-year T-bonds yield 1.7%, interest rates on 2-year T-bonds yield 2.15%, and interest rates on 3-year T-bonds yield 3.8%.

a. It is apparent that today yield on 1-year T-bond is 1.7% and on a 2-year bond is 2.15%. Now, assume that yield on 1-year T-bonds one year from now is x%. Hence, if one invests today at 1.7% for 1-year and at the end of one year, invest the total investment at x%, one should get equivalent of 2.15%.

Therefore (1+0.017)(1+x/100)=(1+0.0215)^2

or 1+x/100=1.04346/1.017=1.026

or x/100=0.026 or x=2.6%

b. For the yield on 2-year T-bonds one year from now, if we invest at 1.7% now and then let us invest in the two year bond after one year at y%, we should get the return equivalent to 3.8% i.e.

(1+0.017)(1+x/100)^2=(1.038)^3

i.e. (1+y/100)^2=1.11839/1.017=1.0997

and 1+y/100=1.04866 i.e. y/100=0.04866 or y=4.866%

c. For the yield on 1-year T-bonds two years from now, one can invest now at 2.15% for two years and then after 2 years say at z% and we should have the same return i.e. 3.8% and in other words

(1+0.0215)^2(1+z/100)=(1+0.038)^3

or 1+z/100=1.11839/1.04346=1.0718 i.e. z/100=0.0718

or z=7.18%