Final answer:
The nominal interest rate on a 7-year Treasury security, when considering the real risk-free rate, the maturity risk premium, and the expected inflation rates, is 7.04%.
Step-by-step explanation:
To calculate the nominal interest rate on a 7-year Treasury security, we need to consider the real risk-free rate, the expected inflation rates over the bond's term, and the maturity risk premium. The given real risk-free rate is 2%. Inflation rates are expected to be 4% in the first year, 5% in the second, and 5% thereafter. The maturity risk premium is given by the formula 0.0003 x (t - 1), where t is the number of years to maturity.
For the first two years, we can simply add the inflation rates to the real risk-free rate:
- Year 1: 2% (real risk-free rate) + 4% (expected inflation) = 6%
- Year 2: 2% (real risk-free rate) + 5% (expected inflation) = 7%
For the remaining years, 5% inflation is expected, so we will use that figure for years 3 through 7.
The maturity risk premium for a 7-year bond is calculated as 0.0003 x (7 - 1) = 0.0018 or 0.18%.
Hence, the nominal interest rate for a 7-year treasury can be estimated by averaging the expected inflation rates over the term and adding the real risk-free rate and the maturity risk premium.
The average expected inflation rate over the 7 years is (4% + 5% + 5% + 5% + 5% + 5% + 5%) / 7 = 4.86%.
The nominal interest rate on a 7-year Treasury security is therefore 2% (real risk-free rate) + 4.86% (average inflation) + 0.18% (maturity risk premium) = 7.04%.
Rounding to two decimal places, the nominal interest rate would be 7.04%.