# Interest and Real Rate

Investment banking firm, is trying to get an idea of what real rate of return investors

Are expecting in today’s marketplace. He has looked up the rate paid on 3-month

U.S. Treasury bills and found it to be 5.5%. He has decided to use the rate of change

In the Consumer Price Index as a proxy for the inflationary expectations of

Investors. That annualized rate now stands at 3%. On the basis of the information

That Carl has collected, what estimate can he make of the real rate of return?

P6–2Real rate of interest To estimate the real rate of interest, the economics division of

Mountain Banks—a major bank holding company—has gathered the data summarized

In the following table. Because there is a high likelihood that new tax legislation

Will be passed in the near future, current data as well as data reflecting the

Probable impacts of passage of the legislation on the demand for funds are also

With passage

Currently of tax legislation

Amount of funds Interest rate Interest rate Interest rate supplied/demanded required by required by required by ($ billion) funds suppliers funds demanders funds demanders

$ 1 2% 7% 9%

5 3 6 8

10 4 4 7

20 6 3 6

50 7 2 4

100 9 1 3

included in the table. (Note: The proposed legislation will not affect the supply schedule of funds. Assume a perfect world in which inflation is expected to be zero, funds suppliers and demanders have no liquidity preference, and all outcomes are certain.)

a. Draw the supply curve and the demand curve for funds using the current data. (Note: Unlike the functions in Figure 6.1 on page 223, the functions here will not appear as straight lines.)

b. Using your graph, label and note the real rate of interest using the current data.

c. Add to the graph drawn in part a the new demand curve expected in the event that the proposed tax legislation is passed.

d. What is the new real rate of interest? Compare and analyze this finding in light of your analysis in part b.

Personal Finance Problem

P6–3Real and nominal rates of interest Zane Perelli currently has $100 that he can

spend today on polo shirts costing $25 each. Alternatively, he could invest the $100

in a risk-free U.S. Treasury security that is expected to earn a 9% nominal rate of

interest. The consensus forecast of leading economists is a 5% rate of inflation over

the coming year.

a. How many polo shirts can Zane purchase today?

b. How much money will Zane have at the end of 1 year if he forgoes purchasing the polo shirts today?

c. How much would you expect the polo shirts to cost at the end of 1 year in light of the expected inflation?

d. Use your findings in parts b and c to determine how many polo shirts (fractions are OK) Zane can purchase at the end of 1 year. In percentage terms, how many more or fewer polo shirts can Zane buy at the end of 1 year?

e. What is Zane’s real rate of return over the year? How is it related to the percentage change in Zane’s buying power found in part d? Explain.

P6–4 Yield curve A firm wishing to evaluate interest rate behavior has gathered yield

data on five U.S. Treasury securities, each having a different maturity and all measured

at the same point in time. The summarized data follow.

U.S. Treasury security Time to maturity Yield

A 1 year 12.6%

B 10 years 11.2

C 6 months 13.0

D 20 years 11.0

E 5 years 11.4

a. Draw the yield curve associated with these data.

b. Describe the resulting yield curve in part a, and explain the general expectations embodied in it.

P6–5 Nominal interest rates and yield curves A recent study of inflationary expectations

has revealed that the consensus among economic forecasters yields the...

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