Question

Suppose the interest rate on a one-year bond today is 

6°/o per year, the interest rate on a one-year bond one 

year from now is expected to be 4°/o per year, and the 

interest rate on a one-year bond two years from now is 

expected to be 3°/o per year. The term premium on a 

two-year bond is 0.5°/o per year and the term premium 

on a three-year bond is 1.0°/o per year. In equilibrium, 

what is the interest rate today on a two-year bond? On 

a three-year bond? What is the shape of the yield 

curve?

Answer 1

Interest rate on a two year bond;

Interest rate=(present interest rate + interest rate one year from now)$\div$ 2 + premium on two year bond.

$=\frac{6\%+4\%}{2}+0.5\%$

$=\frac{10\%}{2}+0.5\%$

$=5.5\%$

Interest rate on a three year bond;

Interest rate=(present interest rate + interest rate two years from now)$\div$ 2 + premium on a three year bond.

$=\frac{6\%+4\%+3\%}{3}+1.0\%$

$=\frac{13\%}{3}+1.0\%$

$=5.33\%$

Shape of the yield curve;

The interest rate on a three year bond is lower than the interest rate on a two year bond thus the curve would shift down