I need to answer the following questions but I also need the equation
needed to arrive at the answer.  Please see below:

1.	The real risk-free rate of interest is 3%.  Inflation is expected
to be 2% this year and 4% during the next 2 years.  Assume that the
maturity risk premium is zero.  What is the yield on 2-year Treasury
securities?  What is the yield on 3-year Treasury securities?
2.	A Treasury bond that matures in 10 years has a yield of 6%.  A 10
year corporate bond has a yield of 8%. Assume that the liquidity
premium on the corporate bond is 0.5%.  What is the default risk
premium on the corporate bond?
3.	One-year Treasury securities yield 5%.  The market anticipates that
1 year from now, 1-year Treasury securities will yield 6%.  If the
pure expectations theory is correct, what should be the yield today
for 2-year Treasury securities?
4.	The real risk-free rate is 3% and inflation is expected to be 3%
for the next 2 years.  A 2-year Treasury security yields 6.2%.  What
is the maturity risk premium for the 2-year security?

1.  The market rate of interest is equal to the real rate of interest
plus the inflation rate plus the product of the real rate of interest
and the inflation rate.

For the two-year security, the average expected inflation is (2% +
4%)/2 = 3%.

For the three-year security, the average expected inflation is (2% +
4% + 4%)/3 = 3 1/3 percent.

So, the yield on the two-year security is equal to 3% + 3% + 3% * 3%
or 6.09%, and the yield on the three-year security is equal to 3% +
3.33% + 3% * 3.33% or 6.433%.

2.  The market rate of interest is equal to the risk-free rate of
interest plus the risk premium.  Treasury bonds are by definition
risk-free, so the risk-free rate of interest is 6%.  Given that the
liquidity premium on the corporate bond is 0.5%, the remaining
difference between the corporate bond's yield and the treasury bond's
yield is the measure of the default risk (there is no relative
inflation risk because both securities have the same duration), which
is 1.5%.

3.  Expectations theory holds that (1 + r1) (1 + E(1r2) = (1 + r2) ^ 2
where r1 is the yield of the one-year security, E(1r2) is the expected
yield of the one-year security one year from now, and r2 is the
current yield of the two-year security.

So, r2 = Square Root [(1.05) (1.06)] - 1 = 5.5%.

4.  Using the formula from problem number 1, we find that the expected
market rate given a risk-free rate of 3% and an expected inflation of
3% is 0.03 + 0.03 + 0.03 * 0.03 or 6.09%.  Using the formula from
problem number 2, we find that the maturity risk premium equals 6.2%
minus 6.09% or 0.11%.

Source: "Principles of Corporate Finance" Fourth Edition by Brealey
and Myers, McGraw-Hill Inc., 1991

Sincerely,

Wonko