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%#