Solutions to the End-of-Chapter Questions, Problems, and Data
Exercises
3.1 The Interest Rate, Present Value, and Future Value
Learning objective: Explain how the interest rate links present value with future value.
Review Questions
1.1 Interest provides lenders with an incentive to supply credit. Interest also compensates lenders for
Problems and Applications
1.5 By describing money as “barren,” Aristotle meant that money does not produce anything by itself.
Lenders should not charge interest on loans, according to Aristotle, because money does not produce
1.6 a. CD 1: $1,000 x (1 + 0.05)3 = $1,157.63
b. A decline in interest rates increases the present value of any future stream of payments, including, in
1.8 a. Money in the future is less valuable than money in the present because: (1) dollars in the future will
b. PV = $22 million/(1 + 0.03)4 = $19.5 million. The author was approximately correct. If the inflation
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Chapter 3 Interest Rates and Rates of Return 23
3.2 Debt Instruments and Their Prices
Learning objective: Distinguish among different debt instruments and understand how their prices are
determined.
Review Questions
2.2 The four basic categories of debt instruments are simple loans, discount bonds, coupon bonds, and
Problems and Applications
2.3 a. Fixed-payment loan
2.4 Fixed-payment loans are popular with households because as long as the household makes all the
payments, the loan will be completely paid off. There will be no large final payment for the
2.5 At time period zero, Ford receives the $1,000 price of the bond. With a 5% coupon rate, Ford pays
2.6 Disagree. The payments on a fixed-payment loan, like the student loan, include both interest and
3.3 Bond Prices and Yield to Maturity
Learning objective: Explain the relationship between the yield to maturity on a bond and its price.
Review Questions
3.1 The yield to maturity is the interest rate that equates the present value of future payments of a
debt instrument with its current price. The yield to maturity is a better measure of the interest rate than
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Chapter 3 Interest Rates and Rates of Return 24
3.2 a.
2 3
… .
(1 ) (1 ) (1 ) (1 ) (1 )
n n
C C C C FV
Pi i i i i
= + + + + +
+ + + + +
c. i
.
F P
P
–
d. Loan value
2
… .
(1 ) (1 ) (1 )
n
FP FP FP
i i i
+ + +
+ + +
Problems and Applications
3.3 At the 10% interest rate:
The present value of $75 one year from now is: $75/(1 + 0.10) = $68.18.
The 20% interest rate compared to the 10% interest rate increase the present value of funds received
sooner. At the 20% interest rate:
The present value of $75 one year from now is: $75/(1 + 0.20) = $62.50.
3.4 The present value of two one-year subscriptions is $60 $60/(1 + 0.10) $114.55. The present
3.5 We now the following must be true for this bond: $870 = $1,000/(1 + i)2. So, we need to solve for
the yield to maturity, i.
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Chapter 3 Interest Rates and Rates of Return 25
3.6 a. $350,000 = $475,000/(1+i)5
b. Thinking in terms of the arithmetic, if David dies after 40 years instead of 20 years, we have to add
3.4 The Inverse Relationship Between Bond Prices and Bond Yields
Learning objective: Understand the inverse relationship between bond prices and bond yields.
Review Questions
4.3 The equation for bond prices on page 62 of the text shows that the higher the purchase price of a
bond, the lower the yield to maturity, and the lower the purchase price of a bond, the higher the yield
4.4 Investors hold a stock, bond, or other security for a long period of time in order to collect the
Problems and Applications
4.5 The price of a bond will be below its face value of $1,000 only if the bond has a coupon rate below
the coupon rates on newly issued bonds. For example, a bond with a coupon rate of 3% will see its
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Chapter 3 Interest Rates and Rates of Return 26
4.6 Disagree. The statement is confusing newly issued bonds with existing bonds. Investors like to
receive higher interest rates when they buy newly issued bonds. But investors suffer losses if they
4.7 a. A coupon rate of 5% means that the bond pays a $50 annual coupon. A bond’s current yield equals
b. The bond’s price is lower than its face value, which raises the yield to maturity above the coupon
4.8 Either conditions in the bond market changed with long-term market interest rates rising, or investors
4.9 No. Increased demand for mortgage-backed bonds increases the prices of these bonds. Because the
4.10 Because both bonds were issued by the U.S. Treasury and have the same maturity date, investors will
Bond a to have a lower higher price than Bond B. Note that even though the two bonds have the
4.11 The analysis is partially correct. There is an inverse relationship between bond prices and bond
3.5 Interest Rates and Rates of Return
Learning objective: Explain the difference between interest rates and rates of return.
Review Questions
5.1 Yield to maturity is the return on a bond assuming the bondholder holds the bond for the full
5.2 Interest-rate risk is the risk that changes in market interest rate will cause changes in the price of a
Problems and Applications
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Chapter 3 Interest Rates and Rates of Return 27
5.3 To calculate the rate of return (R), we need to add the coupon received to the capital gain and divide
5.4 With active secondary markets, Coca-Cola and Walt Disney bonds could be sold before maturity, so
investors other than young people would have an interest in them. Being very long-term bonds, these
5.5 With a coupon rate of 8 3/8 (or 8.375%), you would receive a coupon payment of $83.75. We can
5.6 Because the coupon rate and the market interest rate are the same, the price you paid is equal to the
face value of $1,000. The fall in the market interest rate one year later to 4% increases the present
5.7 a. The present value of the bond is $1,000, so the price is $1,000 and current yield is 6%. When the
b. The in the market interest rate to 5% increases the present value of the payments received from
owning the bond, raising the price of the bond to: $60/(1 + 0.05) + $60/(1 + 0.05)2 + $60/(1 + 0.05)3
c. Investors would be willing to pay a price equal to the present value of the $60 coupon payments for
three years and the face value of $1,000 at the end of three years. With a market interest rate of 5%,
d. Investors would be willing to pay price equal to the present value of the $60 coupon payments for
two years and the face value of $1,000 at the end of two years. With a market interest rate of 10%,
3.6 Nominal Interest Rates Versus Real Interest Rates
Learning objective: Explain the difference between nominal interest rates and real interest rates.
Review Questions
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Chapter 3 Interest Rates and Rates of Return 28
6.3 TIPS, which stands for Treasury Inflation Protection Securities, are indexed bonds, which means that
Problems and Applications
6.4 You would prefer option i. The interest rate of 10% with and expected inflation rate of 8% would be
6.5 The difference between the real interest rate and the expected real interest rate exists because the
future inflation rate is unknown, causing the actual inflation rate to often differ from the expected
6.6 The decline in prices hurt farmers in the late nineteenth century. Deflation was bad for farmers
because they would be paying off their loans with dollars that were increasing in value. The answer
6.7 Yield to maturity (nominal interest rate): (($1,000 $970.87)/$970.87) 100 = 3.00%
6.8 An increase in expected inflation raises nominal interest rates and yields on bonds. Investors require
Data Exercise
D3.1 The gap between the 30-year Treasury bond and the 10-year Treasury note is the greatest during
2010 through 2012. Over the 1990 through 2012 period, the only time the gap exceeds 1 percentage
D3.2 The gap between the nominal and real 1-year Treasury bill rate was the greatest during 1980 and
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Chapter 3 Interest Rates and Rates of Return 29
D3.3 TIPS, Treasury Inflation-Protection Securities, are indexed bonds. The interest rate on the 10-year
Treasury TIPS is an expected real interest rate, while the interest rate on the 10-year Treasury note is
D3.4 a. For December 2012:
Real 30-year Conventional Mortgage Rate = 3.35% – 3.1% = 0.25%
D3.5 a. The 1-year Treasury bill rate for December 2012 is 0.15%, for December 2011 it is 0.11%, and for
December 2010 it is 0.28%. The price of a 1-year $1,000 Treasury bill equals 1000/(1 + i), where i
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