A) To estimate the expected real rate of return on the ten-year U.S Treasury bond, we need to subtract the expected inflation rate from the nominal interest rate.
The nominal interest rate on the ten-year Treasury bond is 2.5 percent.
The expected inflation rate is 1.5 percentage points.
Therefore, the expected real rate of return on the ten-year U.S Treasury bond is:
Real Rate of Return = Nominal Interest Rate - Expected Inflation Rate
= 2.5% - 1.5%
= 1.0%
So, the estimated expected real rate of return on the ten-year U.S Treasury bond is 1.0%.
B) If the real rate of return is expected to be the same for the thirty-year bond, we can use the same 1.0% obtained in the previous calculation.
The nominal interest rate on the thirty-year Treasury bond is 4.0 percent.
We need to estimate the average annual inflation rate expected by investors over the life of the thirty-year bond.
To estimate the average annual inflation rate, we subtract the real rate of return from the nominal interest rate:
Nominal Interest Rate = Real Rate of Return + Expected Inflation Rate
Rearranging the equation, we get:
Expected Inflation Rate = Nominal Interest Rate - Real Rate of Return
= 4.0% - 1.0%
= 3.0%
So, the estimated average annual inflation rate expected by investors over the life of the thirty-year bond is 3.0%.