# 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%.

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 $\left(1 + 0.017\right) \left(1 + \frac{x}{100}\right) = {\left(1 + 0.0215\right)}^{2}$

or $1 + \frac{x}{100} = \frac{1.04346}{1.017} = 1.026$

or $\frac{x}{100} = 0.026$ 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.

$\left(1 + 0.017\right) {\left(1 + \frac{x}{100}\right)}^{2} = {\left(1.038\right)}^{3}$

i.e. ${\left(1 + \frac{y}{100}\right)}^{2} = \frac{1.11839}{1.017} = 1.0997$

and $1 + \frac{y}{100} = 1.04866$ i.e. $\frac{y}{100} = 0.04866$ 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

${\left(1 + 0.0215\right)}^{2} \left(1 + \frac{z}{100}\right) = {\left(1 + 0.038\right)}^{3}$

or $1 + \frac{z}{100} = \frac{1.11839}{1.04346} = 1.0718$ i.e. $\frac{z}{100} = 0.0718$

or z=7.18%