A Treasury note with a maturity of four years carries a nominal rate of interest of 10 percent. In contrast, an eight-year Treasury bond has a yield of 8 percent.

A. If inflation is expected to average 7 percent over the first four years, what is the expected real rate of interest?

B. If the inflation rate is expected to be 5 percent fort he first year, calculate the average annual rate of inflation for years 2 through 4.

C. If the maturity risk premium is expected to be zero between the two Treasury securities, what will be the average annual inflation rate expected over years 5 through 8?

To answer these questions, we need to understand the concept of real interest rate and how it is affected by inflation. The real interest rate is the rate of return on an investment after adjusting for inflation. It is calculated as the nominal interest rate minus the inflation rate.

A. To determine the expected real rate of interest over the first four years, we need to subtract the expected inflation rate from the nominal interest rate. In this case, the nominal rate is 10 percent, and the expected inflation rate is 7 percent. Therefore, the expected real rate of interest can be calculated as follows:

Expected real rate of interest = Nominal rate - Inflation rate
Expected real rate of interest = 10% - 7%
Expected real rate of interest = 3%

Therefore, the expected real rate of interest over the first four years is 3%.

B. To calculate the average annual rate of inflation for years 2 through 4, we need to find the cumulative inflation rate over this period and divide it by the number of years.

Given that the inflation rate for the first year is 5 percent, we need to find the cumulative inflation rate for the years 2 through 4. To do this, we need to know the compound effect of inflation.

First, calculate the cumulative inflation rate for the first year:
Cumulative inflation rate for year 1 = 1 + (Inflation rate / 100)
Cumulative inflation rate for year 1 = 1 + (5 / 100)
Cumulative inflation rate for year 1 = 1.05

Next, calculate the average annual rate of inflation for years 2 through 4:
Average annual rate of inflation for years 2-4 = (Cumulative inflation rate for year 1-4)^(1/3) - 1
Average annual rate of inflation for years 2-4 = (1.05^4)^(1/3) - 1
Average annual rate of inflation for years 2-4 ≈ (1.2155064)^(1/3) - 1
Average annual rate of inflation for years 2-4 ≈ 1.053 - 1
Average annual rate of inflation for years 2-4 ≈ 5.3%

Therefore, the average annual rate of inflation for years 2 through 4 is 5.3%.

C. To determine the average annual inflation rate expected over years 5 through 8, we need to use the yield of the eight-year Treasury bond. The yield represents the market's expectation of the average annual return on the bond.

Given that the yield on the eight-year Treasury bond is 8 percent, it already incorporates the expected inflation rate. Therefore, we can directly take the yield as the expected average annual inflation rate over years 5 through 8.

Therefore, the average annual inflation rate expected over years 5 through 8 is 8%.