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The real risk-free rate is $3.0\%$ and inflation is expected to be $3.25\%$ for the next $2$ years. A $2$ -year Treasury security yields $6.55\%$ . What is the maturity risk premium for the $2$ -year security?

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Exponential growth and decay: word problems

Full solution

Q. The real risk-free rate is

3.0\%

and inflation is expected to be

3.25\%

for the next

2

years. A

2

-year Treasury security yields

6.55\%

. What is the maturity risk premium for the

2

-year security?

Understand Fisher Equation: Understand the Fisher Equation which relates the real risk-free rate, the inflation rate, and the nominal rate (yield on the Treasury security). The Fisher Equation is: Nominal rate $=$ Real risk-free rate $+$ Inflation rate $+$ Maturity risk premium. We need to find the Maturity risk premium.
Identify Given Values: Identify the given values from the problem. $\newline$ Real risk-free rate = $3.0\%$ $\newline$ Inflation rate = $3.25\%$ $\newline$ Nominal rate (yield on the $2$ -year Treasury security) = $6.55\%$
Insert Values and Solve: Insert the given values into the Fisher Equation and solve for the Maturity risk premium. $6.55\% = 3.0\% + 3.25\% +$ Maturity risk premium
Subtract to Find Premium: Subtract the sum of the real risk-free rate and the inflation rate from the nominal rate to find the Maturity risk premium. $\newline$ Maturity risk premium = $6.55\% - (3.0\% + 3.25\%)$
Perform Calculation: Perform the calculation. $\newline$ Maturity risk premium $= 6.55\% - 6.25\%$ $\newline$ Maturity risk premium $= 0.30\%$

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