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Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets, Twelfth Edition 73
Chapter 4
ANSWERS TO QUESTIONS
1. Would a dollar tomorrow be worth more to you today when the interest rate is 20% or when
it is 10%?
2. Explain which information you would need to take into consideration when deciding to
receive $5,000 today or $5,500 one year from today.
3. To help pay for college, you have just taken out a $1,000 government loan that makes you
pay $126 per year for 25 years. However, you don’t have to start making these payments
until you graduate from college two years from now. Why is the yield to maturity necessarily
less than 12%? (This is the yield to maturity on a normal $1,000 fixed-payment loan on
which you pay $126 per year for 25 years.)
4. Do bondholders fare better when the yield to maturity increases or when it decreases? Why?
5. Suppose today you buy a coupon bond that you plan to sell one year later. Which part of the
rate of return formulation incorporates future changes into the bond?
Note: Check Equations 7 and 8 in this chapter.
Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets, Twelfth Edition 76
17. Suppose that a commercial bank wants to buy Treasury bills. These instruments pay $5,000 in
one year and are currently selling for $5,012. What is the yield to maturity of these bonds? Is
this a typical situation? Why?
The yield to maturity of these bonds solves the following equation: 5,000/(1+i) = 5,012.
18. What is the yield to maturity on a simple loan for $1 million that requires a repayment of $2
million in five years’ time?
19. Which $1,000 bond has the higher yield to maturity, a twenty-year bond selling for $800 with
a current yield of 15% or a one-year bond selling for $800 with a current yield of 5%?
If the one-year bond did not have a coupon payment, its yield to maturity would be ($1,000 –
$800)/ $800 = $200/$800 = 0.25, or 25%. Because it does have a coupon payment, its yield
20. Consider a bond with a 4% annual coupon and a face value of $1,000. Complete the
following table. What relationships do you observe between years to maturity, yield to
maturity, and the current price?
Years to Maturity
Yield to Maturity
Current Price
2
2%
2
4%
3
4%
5
2%
5
6%
Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets, Twelfth Edition 77
Years to Maturity
Yield to Maturity
Current Price
2
2%
1038.83
2
4%
1000.00
3
4%
1000.00
5
2%
1094.27
5
6%
915.75
21. Consider a coupon bond that has a $1,000 par value and a coupon rate of 10%. The bond is
currently selling for $1,044.89 and has two years to maturity. What is the bond’s yield to
maturity?
When yield to maturity is above the coupon rate, the bond’s current price is below its face
22. What is the price of a perpetuity that has a coupon of $50 per year and a yield to maturity of
2.5%? If the yield to maturity doubles, what will happen to the perpetuity’s price?
23. Property taxes in a particular district are 4% of the purchase price of a home every year. If
you just purchased a $250,000 home, what is the present value of all the future property tax
payments? Assume that the house remains worth $250,000 forever, property tax rates never
change, and a 6% interest rate is used for discounting.
24. A $1000-face-value bond has a 10% coupon rate, its current price is $960, and its price is
expected to increase to $980 next year. Calculate the current yield, the expected rate of
capital gain, and the expected rate of return.
25. Suppose that you want to take out a loan and that your local bank wants to charge you an
annual real interest rate equal to 3%. Assuming that the annualized expected rate of inflation
over the life of the bond is 1%, determine the nominal interest rate that the bank will charge
you. What happens if, over the life of the loan, actual inflation is 0.5%?
Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets, Twelfth Edition 78
ANSWERS TO DATA ANALYSIS PROBLEMS
1. Go to the St. Louis Federal Reserve FRED database and find data on the interest rate on a
four-year auto loan (TERMCBAUTO48NS). Assume that you borrow $20,000 to purchase a
new automobile and that you finance it with a four-year loan at the most recent interest rate
given in the database. If you make one payment per year for four years, what will the yearly
payment be? What is the total amount that will be paid out on the $20,000 loan?
2. The U.S. Treasury issues some bonds as Treasury Inflation Indexed Securities, or TIIS, which
are bonds adjusted for inflation; hence the yields can be roughly interpreted as real interest
rates. Go to the St. Louis Federal Reserve FRED database and find data on the following
TIIS bonds and their nominal counterparts. Then answer the questions below.
• 5 year U.S. treasury (DGS5) and 5-year TIIS (DFII5)
• 7 year U.S. treasury (DGS7) and 7-year TIIS (DFII7)
• 10 year U.S. treasury (DGS10) and 10-year TIIS (DFII10)
• 20 year U.S. treasury (DGS20) and 20-year TIIS (DFII20)
• 30 year U.S. treasury (DGS30) and 30-year TIIS (DFII30)
a. Following the Great Recession of 2008–2009, the 5, 7, 10, and even the 20-year TIIS
yields became negative for a period of time. How is this possible?
b. Using the most recent data available, calculate the difference between the yields for each
of the pairs of bonds (DGS5 – DFII5, etc.) listed above. What does this difference
represent?
Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets, Twelfth Edition 79
Copyright © 2019 by Pearson Education, Inc. All rights reserved.
The difference between the pairs represents expected inflation over the relevant bond
horizon. Calculations for June 29, 2017, are shown below.
29-Jun-17
Nominal
TIIS
Difference (Inflation
Expectations)
5 Year
1.85
0.23
1.62
7 Year
2.10
0.43
1.67
10 Year
2.27
0.55
1.72
20 Year
2.59
0.81
1.78
30 Year
2.82
0.96
1.86
c. Based on your answer to part (b), are there significant variations among the differences
in the bond-pair yields? Interpret the magnitude of the variation in differences among the
pairs.
