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# Real Rate of Return, Expected Nominal Interest Rate

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1) Assume investors expect a 2.0 percent real rate of return over the next year. If the inflation is expected to be 0.5 percent, what is the expected nominal interest rate for a one-year U.S. Treasury security?

2) A thirty-year U.S. Treasury bond has a 4.0 percent interest rate. In contrast, a ten-year Treasury bond has an interest rate of 3.7 percent. If inflation is expected to average 1.5 percentage points over both the next ten years and thirty years, determine the maturity risk premium for the thirty-year bond over the ten-year bond.

3) You are considering an investment in a one-year government debt security with a yield of 5 percent or a highly liquid corporate debt security with a yield of 6.5 percent. The expected inflation rate for the next year is expected to be 2.5 percent.

a. What would be your real rate earned on either of the two investments?
b. What would be the default risk premium on the corporate debt security?

4) 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?

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#### Solution Preview

Hi there,

I have answered your questions in file: 520202 Rate of Return. I added some comments between answers to help explain the concepts.
** Please see the attached file for docx. formatted copy of the solution **

1) Assume investors expect a 2.0 percent real rate of return over the next year. If inflation is expected to be 0.5 percent, what is the expected nominal interest rate for a one-year U.S. Treasury security?
Expected nominal interest rate: 1.5 %
Comments
Two different interest rates are used in the discussion of loans. The nominal interest rate is the reported rate. This rate does not take into account the effects of inflation. The real interest rate is not usually reported. This real interest rate takes into account the effects of inflation on the purchasing power of money repaid from a loan.

2) A thirty-year U.S. Treasury bond has a 4.0 percent interest rate. In contrast, a ten-year Treasury bond has an interest rate of 3.7 percent. If inflation is expected to average 1.5 percentage points over both the ...

#### Solution Summary

This solution provides a calculation of expected nominal interest rate and maturity risk premium, and includes comments on the real rate earned and the default risk premium.

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