Interest and Real Rate

Topics: Interest, Yield curve, Bond Pages: 9 (1754 words) Published: January 5, 2013
P6–1Interest rate fundamentals: The real rate of return Carl Foster, a trainee at an
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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