63. The coupon rate for a coupon bond is equal to the:
a. annual coupon payment divided by the face value of the bond.
b. annual coupon payment divided by the purchase price of the bond.
c. purchase price of the bond divided by the coupon payment.
d. annual coupon payment divided by the selling price of the bond.
64. If a bond has a face value of $1,000 and a coupon rate of 4.25%, the bond owner will receive
annual coupon payments of:
a. $425.00
b. $4.25
c. $42.50
d. a value that cannot be determined from the information provided.
65. If a bond has a face value of $1,000 and the bondholder receives coupon payments of $27.50
semi-annually, the bond’s coupon rate is:
a. 2.75%
b. 5.50%
c. 27.5%
d. a value that cannot be determined from the information provided.
66. Consider a bond that costs $1,000 today and promises a one-time future payment of $1,080 in
four years. What is the approximate interest rate on this bond?
a. 2%
b. 4%
c. 8%
d. 10.8%
67. Which of the following is necessarily true of coupon bonds?
a. The price exceeds the face value.
b. The coupon rate exceeds the interest rate.
c. The price is equal to the coupon payments.
d. The price is the sum of the present value of coupon payments and the face value.
68. The price of a coupon bond will increase as the:
a. face value decreases.
b. yield increases.
c. coupon payments increase.
d. term to maturity is shorter.
69. Suppose the nominal interest rate on a one-year car loan is 8% and the inflation rate is
expected to be 3% over the next year. Based on this information, we know:
a. the ex ante real interest rate is 5%.
b. the lender benefits more than the borrower because of the difference in the nominal versus real
interest rates.
c. at the end of the year, the borrower pays only 5% in nominal interest.
d. the ex post real interest rate 11%.
70. Interest rates that are adjusted for expected inflation are known as:
a. coupon rates.
b. ex ante real interest rates.
c. ex post real interest rates.
d. nominal interest rates.
71. The price of a coupon bond is determined by taking the present value of:
a. the bond’s final payment and subtracting the coupon payments.
b. the coupon payments and adding this to the face value.
c. the bond’s final payment.
d. all of the bond’s payments.
72. The price of a coupon bond is determined by:
a. taking the present value of the bond’s final payment and subtracting the coupon payments.
b. taking the present value of the coupon payments and adding this to the face value.
c. taking the present value of all of the bond’s payments.
d. estimating its future value.
73. Compounding refers to the
a. calculation of after tax interest returns.
b. internal rate of return a firm earns on an investment.
c. real interest return after taxes.
d. process of earning interest on both the principal and the interest of an investment.
74. The interest rate that equates the price of a bond with the present value of its payments:
a. will vary directly with the value of the bond.
b. should be the one that makes the value equal to the par value of the bond.
c. will vary inversely with the value of the bond.
d. should always be greater than the coupon rate.
75. A credit card that charges a monthly interest rate of 1.5% has an effective annual interest rate
of:
a. 18.0%
b. 19.6%
c. 15.0%
d. 17.50%
76. Which formula below best expresses the real interest rate, (r)?
a. i = r –
e
b. r = i +
e
c. r = i –
e
d.
e = i + r
77. A borrower who makes a $1,000 loan for one year and earns interest in the amount of $75,
earns what nominal interest rate and what real interest rate if inflation is two percent?
a. A nominal rate of 5.5% and a real rate of 2.0%.
b. A nominal rate of 7.5% and a real rate of 5.0%.
c. A nominal rate of 7.5% and a real rate of 9.5%.
d. A nominal rate of 7.5% and a real rate of 5.5%.
78. As inflation increases, for any fixed nominal interest rate, the real interest rate:
a. also increases.
b. remains the same, that’s why it is real.
c. decreases.
d. decreases by less than the increase in inflation.
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79. Considering the data on real and nominal interest rates for the U.S. from 1979 to 2012, which
of the following statements is most accurate?
a. The real interest rate remains unchanged over time.
b. There have been times when the real interest rate has been negative.
c. Nominal interest rates higher in 2000 than they had been at any other point in time.
d. The inflation rate is always greater than the real interest rate.
80. Which of the following statements is most correct?
a. We can always compute the ex post real interest rate but not the ex ante real rate.
b. We cannot compute either the ex post or ex ante real interest rates accurately.
c. We can accurately compute the ex ante real interest rate but not the ex post real rate.
d. None of the statements are correct.
81. From the Fisher equation we see that the nominal interest rate and expected inflation have:
a. an inverse relationship.
b. a relationship which is direct but less than one-to–one.
c. a relationship which is direct and one-to-one.
d. no relationship.
82. If a lender wants to earn a real interest rate of 3% and expects inflation to be 3%, he/she
should charge a nominal interest rate that:
a. is at least 7%.
b. is anything above 0%.
c. equals the real rate desired plus expected inflation.
d. equals the real rate desired less expected inflation.
83. We should expect a country that experiences volatile inflation to also have:
a. volatile nominal interest rates.
b. volatile real interest rates but stable nominal rates.
c. stable nominal interest rates.
d. volatile real interest rates.
Short Answer Question
84. A lender expects to earn a real interest rate of 4.5% over the next 12 months. She charges a
9.25% (annual) nominal rate for a 12-month loan. What inflation rate is she expecting? If the
lender is in a 30% marginal tax bracket, the borrower in a 25% marginal tax bracket, and they both
have the same inflation expectations, what are the real after-tax rates each expects?
85. Compute the interest rate for a $1,000 face value a bond that sells for $280 and matures in
20 years. The bond has no coupon payments, only the face value payment.
86. Compute the future value of $1,000 at a 6 percent interest rate after three different lengths of
time. Use 6, 10 and 20 years into the future.
87. Considering the concept of compounding, explain why in determining the future value of a
$100 investment at 5 percent annual interest, you can’t simply multiply $100 by (1.10) and get the
correct answer.
88. Calculate which has a higher present value: an annual payment of $100 received over 3
years or an annual payment of $50 received over 7 years. In both cases the interest rate is 7% (or
0.07).
89. What is the monthly interest rate if you are asked to convert a 12 percent annual rate to a
monthly rate (calculate to 4 decimal places)?
90. Convert each of the following basis points amounts to percents:
a) 412.5
b) 10
c) 125.7
d) 1075
e) 1
91. Using the rule of 72, determine the approximate time it will take $1,000 to double given the
following interest rates.
a) 5.5%
b) 10.0%
c) 30.0%
d) 2.0%
e) 4.5%
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92. What will be the amount owed at the end of one year if a borrower charges $100 on his/her
credit card and doesn’t make any payments during the year (assume the interest rate is 1.5% per
month)?
93. Which investment plan will provide the highest future value: $500 invested at 5 percent
annually for four years and then that balance invested at 7 percent annually for an additional three
years, or $500 invested at 6 percent annually for seven years?
94. Suppose that you have a winning lottery ticket for $100,000. The State of California doesn’t
pay this amount up front – this is the amount you will receive over time. The State offers you two
options. The first pays you $80,000 up front and that will be the entire amount. The second pays
you winnings over a three year period. The last option pays you a large payment today with
small payments in the future. The payment options are detailed in the table below:
Compute the present value of each payment option, assuming the interest rate is 12%. Now,
compute the present values based on an interest rate of 5%. Compare your answers, explaining
why they are different when the interest rate changes. When the interest rate is 5%, the present
values are as follows:
95. Briefly discuss the relationship between present value and each of the following:
a) future value
b) time
c) interest rate
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96. An investment grows from $2,000 to $2,750 over the period of 10 years. What average annual
growth rate will produce this result?
97. Calculate the internal rate of return for a machine that costs $500,000 and provides annual
revenue of $115,000 per year for 5 years. You can assume all revenue is received once a year at
the end of the year.
98. You win your state lottery. The lottery officials offer you the following options: you can
accept annual payments of $50,000 for 20 years or receive an upfront payment of $700,000.
Ignoring issues like mortality tables, taxes, etc.; and assuming the first payment is made
immediately, what market interest rate would make it more attractive to take the upfront payment?
99. You are considering purchasing a home. You find one that you like but you realize that you
will need to obtain a mortgage for $100,000. The mortgage company presents you with two
options: a 15-year mortgage at a 6.0% annual rate and a 30-year mortgage at a 6.5% annual rate.
What will be the fixed annual payment for each mortgage?
100. A bond offers a $50 coupon, has a face value of $1,000, and has 10 years to maturity. If the
interest rate is 4.0% what is the value of this bond?
101. A bond offers a $40 coupon, has a face value of $1,000, and 10 years to maturity. If the
interest rate is 5.0%, what is the value of this bond?
102. Suppose a two-year coupon bond has payments of $40 and a face value of $800. The interest
rate is 8%. Compute the present value of the coupon payments and the principal payment of the
bond. What is the price of this bond?
103. Suppose you negotiate a one-year loan with a principal of $1000 and the nominal interest
rate is currently 7%. You expect the inflation rate to be 3% over the next year. When you repay the
principal plus interest at the end of the year, the actual inflation rate is 2.5%. Compute the ex ante
and ex post real interest rate. Who benefits from this unexpected decrease in inflation? Who loses?
104. In the data, we observe that countries with high inflation rates tend to have high nominal
interest rates. What does this imply, if anything, about real interest rates in countries with very
high inflation rates?
105. Explain why an increase in expected inflation will result in an increase in nominal interest
rates, holding other factors constant.
106. Explain why, if real interest rates are so important, we see most interest rates quoted in
nominal terms.
107. If a borrower and a lender agree on a long-term loan at a nominal interest rate that is fixed
over the duration of the loan, how will a higher-than-expected rate of inflation impact the parties if
at all?
108. Explain why countries with high and volatile inflation rates are likely to have volatile
nominal interest rates.
109. Explain why the Fisher equation is not highly accurate at high rates of inflation. Use an
example.
110. An individual is currently 30 years old, wants to work until the age of 65 and plans on dying
at the age of 85. How much will the individual need to have saved by the time he or she is
65 if he or she plans on spending $40,000 per year while retired? You can assume the individual
can earn an interest rate of 5.0% and the $40,000 is in addition to any Social Security that may be
received.
111. How might the behavior of professional investment managers prior to the financial crisis of
2007-2009 contributed to the depth of the plunge of corporate and mortgage security prices during
the crisis?
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Essay Questions
112. Explain why an investor cannot simply compare the size of promised payments from different
investments, even if the interest rates and other risk factors are the same.
113. Historically, many cultural groups have outlawed usury, or the practice of levying interest on
loans. Some groups oppose usury because it exacerbates problems of income inequality (as
wealthier individuals can afford to lend to poorer individuals), while others claim investment and
loans should be made charitably. Evaluate these arguments against usury based on your knowledge
of present value. Do such prohibitions make sense?
114. How has Islamic banking redefined lending to deal with Islam’s prohibition of usury?
115. Discussions in recent years about the vulnerability of the Social Security System cause some
people to feel the payments promised will not materialize. Discuss the possible changes we might
observe now.
116. During the early 1980s, the U.S. economy experienced an increase in interest rates quoted on
U.S. Treasury debt, business loans, and mortgages. At the same time the inflation rate gradually
declined more than expected. What happened to ex ante versus ex post real interest rates during
this period? Use the Fisher equation to support your answer.
117. Explain why countries that have volatile inflation rates are likely to have high nominal
interest rates.
118. Explain the suggestion that people may have their own “personal discount rate” and how that
may affect decisions about borrowing and other financial matters.