Chapter 04 – Future Value, Present Value, and Interest Rates
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97. 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.
Chapter 04 – Future Value, Present Value, and Interest Rates
98. Briefly discuss the relationship between present value and each of the following:
a) future value
b) time
c) interest rate
99. An investment grows from $2,000 to $2,750 over the period of 10 years. What average
annual growth rate will produce this result?
Chapter 04 – Future Value, Present Value, and Interest Rates
100. 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.
101. 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., what market interest rate would make it more
attractive to take the upfront payment?
102. 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?
Chapter 04 – Future Value, Present Value, and Interest Rates
103. 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?
104. A bond offers a $40 coupon, has a face value of $1000, and 10 years to maturity. If the
interest rate is 5.0%, what is the value of this bond?
105. Describe the effects on the value of a bond from the following: length of time to maturity
and interest rates (you can ignore the relationship of the coupon rate to market interest rates to
simplify the analysis).
Chapter 04 – Future Value, Present Value, and Interest Rates
106. 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?
107. 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?
Chapter 04 – Future Value, Present Value, and Interest Rates
108. 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?
109. Explain why an increase in expected inflation will result in an increase in nominal
interest rates, holding other factors constant.
110. Explain why, if real interest rates are so important, we see most interest rates quoted in
nominal terms.
Chapter 04 – Future Value, Present Value, and Interest Rates
111. 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?
112. Explain why countries with high and volatile inflation rates are likely to have volatile
nominal interest rates.
Chapter 04 – Future Value, Present Value, and Interest Rates
113. Explain why the Fisher equation is not highly accurate at high rates of inflation. Use an
example.
114. 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.
Chapter 04 – Future Value, Present Value, and Interest Rates
115. 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?
Essay Questions
116. 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.
Chapter 04 – Future Value, Present Value, and Interest Rates
117. 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?
118. How has Islamic banking redefined lending to deal with Islam’s prohibition of usury?
Chapter 04 – Future Value, Present Value, and Interest Rates
119. 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.
120. 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.
Chapter 04 – Future Value, Present Value, and Interest Rates
121. Explain why countries that have volatile inflation rates are likely to have high nominal
interest rates.
122. Explain the suggestion that people may have their own “personal discount rate” and how
that may affect decisions about borrowing and other financial matters.
Chapter 04 – Future Value, Present Value, and Interest Rates
123. What matters more: having a credit card with a low rate or paying off your balance as
quickly as possible? Explain.