12. 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 for the 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?
a. To calculate the expected real rate of interest, we need to subtract the expected inflation rate from the nominal rate of interest. In this case, the nominal rate of interest is 10 percent and the expected inflation rate is 7 percent.
Real rate of interest = Nominal rate of interest - Expected inflation rate
Real rate of interest = 10% - 7%
Real rate of interest = 3%
Therefore, the expected real rate of interest is 3%.
b. To calculate the average annual rate of inflation for years 2 through 4, we need to find the average of the individual inflation rates for each year. We know that the inflation rate for the first year is 5 percent. Let's assume the inflation rates for years 2, 3, and 4 are x1, x2, and x3 respectively.
Average annual rate of inflation for years 2 through 4 = (5% + x1 + x2 + x3)/3
Unfortunately, the information provided does not give us any specific values for x1, x2, and x3. Therefore, it is not possible to calculate the average annual rate of inflation for years 2 through 4 with the given information.
c. To calculate the average annual inflation rate expected over years 5 through 8, we need to compare the yield of the eight-year Treasury bond (8%) with the nominal rate of interest on a new four-year Treasury note. Since the maturity risk premium is expected to be zero between the two Treasury securities, we can assume that the nominal rate on the new four-year Treasury note would also be 8%.
Since the nominal rate of interest and the yield are both 8%, there is no difference in interest rates due to the maturity of the bond. Therefore, the average annual inflation rate expected over years 5 through 8 would be the same as the nominal rate of interest, which is 8%.