Question

The real risk-free rate is 3.15%. Inflation is expected to be 2.45% this year, 3.75% next year, and 2% thereafter. The maturity risk premium is estimated to be 0.05 × (t - 1)%, where t = number of years to maturity. What is the yield on a 7-year Treasury note? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Given the following information,

Real risk free rate = 3.15%

We know that

Inflation premium = Average inflation rate over 7 years

Inflation premium = (2.45% + 3.75% + 2% + 2% + 2% + 2% + 2% )/7

Inflation premium = (16.2% )/7

Inflation premium = 2.31%

Market risk premium = 0.05 × (t - 1)%

Where t = 7

Substituting t in the above equation,

Market risk premium = 0.05 × (7 - 1)%

Market risk premium = 0.05 × (6)%

Market risk premium = 0.3%

The yield on a 7 year treasury bond is calculated using the following formula,

Yield on 7-year Treasury Note = Real Risk-free Rate + Inflation Premium + Maturity Risk Premium

Yield on 7-year Treasury Note = 3.15% + 2.31% + 0.3%

Yield on 7-year Treasury Note = 5.76%

Therefore, the yield on a 7 year treasury bond is 5.76%