CHAPTER 4
Understanding Interest Rates
83
measures are misleading guides to the size of the
interest rate, a change in them always signals a change
in the same direction for the yield to maturity.
3.
The return on a security, which tells you how well you
have done by holding this security over a stated period
of time, can differ substantially from the interest rate as
measured by the yield to maturity. Long-term bond
prices have substantial fluctuations when interest rates
change and thus bear interest-rate risk. The resulting
capital gains and losses can be large, which is why long-
term bonds are not considered to be safe assets with a
sure return.
4.
The real interest rate is defined as the nominal interest
rate minus the expected rate of inflation. It is a better
measure of the incentives to borrow and lend than the
nominal interest rate, and it is a more accurate indicator
of the tightness of credit market conditions than the
nominal interest rate.
Key Terms
basis point, p. 74
consol or perpetuity, p. 67
coupon bond, p. 63
coupon rate, p. 64
current yield, p. 70
discount bond (zero-coupon bond),
p. 64
face value (par value), p. 63
fixed-payment loan (fully amortized
loan), p. 63
indexed bond, p. 82
interest-rate risk, p. 78
nominal interest rate, p. 79
present discounted value, p. 61
present value, p. 61
rate of capital gain, p. 76
real interest rate, p. 79
real terms, p. 80
return (rate of return), p. 75
simple loan, p. 62
yield on a discount basis (discount
yield), p. 71
yield to maturity, p. 64
Questions and Problems
Questions marked with an asterisk are answered at the end
of the book in an appendix,
“
Answers to Selected Questions
and Problems.
”
*1.
Would a dollar tomorrow be worth more to you today
when the interest rate is 20% or when it is 10%?
2.
You have just won $20 million in the state lottery,
which promises to pay you $1 million (tax free) every
year for the next 20 years. Have you really won $20
million?
*3.
If the interest rate is 10%, what is the present value of
a security that pays you $1,100 next year, $1,210 the
year after, and $1,331 the year after that?
4.
If the security in Problem 3 sold for $3,500, is the
yield to maturity greater or less than 10%? Why?
*5.
Write down the formula that is used to calculate the
yield to maturity on a 20-year 10% coupon bond with
$1,000 face value that sells for $2,000.
6.
What is the yield to maturity on a $1,000-face-value
discount bond maturing in one year that sells for
$800?
*7.
What is the yield to maturity on a simple loan for $1
million that requires a repayment of $2 million in five
years
’
time?
8.
To 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 necessar-
ily less than 12%, the yield to maturity on a normal
$1,000 fixed-payment loan in which you pay $126