# Inflation and Real Rate of Return

1. A man bought a 5% tax-free municipal bond. It cost $1000 and will pay $50 interest each year for 20 years. At maturity the bond returns the original $1000. There is 2% annual inflation. what real rate of interest will the investor receive?

1. What rate of return will the investor receive after the effect of inflation has been accounted for?

2. What will be the value in current dollars of the $1000 the man will receive in 20 years?

2. A man wishes to set aside some money for his daughter's college education. His goal is to have a bank savings account containing an amount equivalent to $20,000 in today's dollars at the girl's 18th birthday. The estimated inflation rate is 8%. The bank pays 5% compounding annually..

1. How much in then current dollars will be required to have an amount equivalent to $20,000 today?

2. Assume that after the man calculates that he will have to deposit more than $29,000 to have $20,000 buying power in 14 years, he finds another bank that will pay him 6%. How much will he have to deposit in the new bank?

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#### Solution Preview

1:

1. 2.9%. Please refer to attached excel file for calculations.

2. Value of $1000 in current dollars=FV/(1+inflation rate)^no. of ...

#### Solution Summary

There are two problems. Solution to first problem depicts the methodology to calculate the inflation adjusted rate of return and future value in current dollars. Solution to second problem describes the steps to estimate the future value in current dollars.

Real Rate of Return, Expected Nominal Interest Rate

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?