© 2013 Pearson Education, Inc. All rights reserved.4-1 Money & Banking Video 03—Interest Rates...
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Transcript of © 2013 Pearson Education, Inc. All rights reserved.4-1 Money & Banking Video 03—Interest Rates...
© 2013 Pearson Education, Inc. All rights reserved. 4-1
Money & Banking
Video 03—Interest Rates
Understanding interest rates (Chapter 4)
Hal W. Snarr8/20/2015
Chapter 4
Understanding Interest Rates
© 2013 Pearson Education, Inc. All rights reserved. 4-3
Measuring Interest Rates
Discount rate – the rate used to weigh a stream of future payments
• Most choices require decision-makers to trade-off costs and benefits at different points in time (e.g., savings, work effort, education, projects…)
• As the payment gets further and further into the future, people tend to place less and less weight on it
• People who are more worried about Right Now, discount the future more than those who are concerned more with the future
• In economics, the discount rate is determined by o market rate of interest io one’s time preference
© 2013 Pearson Education, Inc. All rights reserved. 4-4
If discount rate i represents a time preference, the present value of a stream of future payments is
Present Value
31 21 2 3
. . . (1 ) (1 ) (1 ) (1 )
nn
P i
F
i
F
i i
F F
P = present value of a discounted stream of paymentsFi = dollar value of a future payment received at the END of period in = years to maturity date
© 2013 Pearson Education, Inc. All rights reserved. 4-5
If discount rate i represents a time preference, the present value of a stream of future payments is
P = present value of a discounted stream of paymentsFi = dollar value of a future payment received at the START of period in = years to maturity date
0 131 2
2 1 . . .
(1 ) (1 ) (1 ) (1 )nnP
i
F F
i
F
i i
F
Present Value
© 2013 Pearson Education, Inc. All rights reserved. 4-6
If discount rate i represents a time preference, the present value of a stream of future payments is
0 131 2
2 1 . . .
(1 ) (1 ) (1 ) (1 )nnP
i
F F
i
F
i i
F
Example: Suppose a person with a monthly discount rate of 0.4% wins a lottery. When the winner is announced, the winner can choose one check in the amount of $1,000,000, or checks in the amount of $10,000 each month for the next 10 years. Either way, the person leaves the building with a huge check in hand. Which option will the winner choose?
Present Value
© 2013 Pearson Education, Inc. All rights reserved. 4-7
If discount rate i represents a time preference, the present value of a stream of future payments is
0 1 2 119 . . .
(1 ) (1 ) (1 )
1000000
.004 .004 .0
0 0 0
(04 041 ).0P
Example: Suppose a person with a monthly discount rate of 0.4% wins a lottery. When the winner is announced, the winner can choose one check in the amount of $1,000,000, or checks in the amount of $10,000 each month for the next 10 years. Either way, the person leaves the building with a huge check in hand. Which option will the winner choose?
Present Value
© 2013 Pearson Education, Inc. All rights reserved. 4-8
If discount rate i represents a time preference, the present value of a stream of future payments is
100 0000P
Example: Suppose a person with a monthly discount rate of 0.4% wins a lottery. When the winner is announced, the winner can choose one check in the amount of $1,000,000, or checks in the amount of $10,000 each month for the next 10 years. Either way, the person leaves the building with a huge check in hand. Which option will the winner choose?
Present Value
© 2013 Pearson Education, Inc. All rights reserved. 4-9
If discount rate i represents a time preference, the present value of a stream of future payments is
Example: Suppose a person with a monthly discount rate of 0.4% wins a lottery. When the winner is announced, the winner can choose one check in the amount of $1,000,000, or checks in the amount of $10,000 each month for the next 10 years. Either way, the person leaves the building with a huge check in hand. Which option will the winner choose?
0 1 2 119
10000 10000 100 . . .
(1 ) (1 ) (1 ).004 .
00 10000
004 . (1004 .004)P
M&B_lottery.xlsx
Present Value
© 2013 Pearson Education, Inc. All rights reserved. 4-10
If discount rate i represents a time preference, the present value of a stream of future payments is
Example: Suppose a person with a monthly discount rate of 0.4% wins a lottery. When the winner is announced, the winner can choose one check in the amount of $1,000,000, or checks in the amount of $10,000 each month for the next 10 years. Either way, the person leaves the building with a huge check in hand. Which option will the winner choose?
955,365.92 P
M&B_lottery.xlsx
Present Value
© 2013 Pearson Education, Inc. All rights reserved. 4-11
If discount rate i represents a time preference, the present value of a stream of future payments is
Example: Suppose a person with a monthly discount rate of 0.4% wins a lottery. When the winner is announced, the winner can choose one check in the amount of $1,000,000, or checks in the amount of $10,000 each month for the next 10 years. Either way, the person leaves the building with a huge check in hand. Which option will the winner choose?
955,365.92 P
The winner chooses the $1,000,000 check
M&B_lottery.xlsx
Present Value
© 2013 Pearson Education, Inc. All rights reserved. 4-12
18 6522Age
40,000
16,000
-5,000
Dollars/year
Goes to College
Only High School
0
A person who gets a HS diploma earns $16,000 a year from age 18 until he/she retires. If the person goes to college, • he/she pays $20,000 in tuition• foregoes earning $64,000 • but earns $1,032,000 more by graduating from college from age 22 to age 64.
(24,000/year)(43 years) = $1,032,000
$20,000 $64,000 + = $84,000
Why do people invest in HUMAN capital?
© 2013 Pearson Education, Inc. All rights reserved. 4-13
1 2 3 4
5,000 5,000 5,000 5,000$12,944
(1 0.2) (1 0.2) (1 0.2) (1 0.2)BS cost
womenPV
1 2 47
16,000 16,000 16,000... $79,985
(1 0.2) (1 0.2) (1 0.2)HS earnings
womenPV
The previous model ignores the discount rate• Swann (2003) estimates the annual discount rate of women at 20%
• Keane and Wolpin (1997) estimate the discount rate of young men at 28%
1 2 47
16,000 16,000 16,000... $57,142
(1 0.28) (1 0.28) (1 0.28)HS earnings
menPV
1 2 3 4
5,000 5,000 5,000 5,000$11,205
(1 0.28) (1 0.28) (1 0.28) (1 0.28)BS cost
menPV
Why do people invest in HUMAN capital?
5 6 47
40,000 40,000 40,000... $96,413
(1 0.2) (1 0.2) (1 0.2)BS earnings
womenPV
5 6 47
40,000 40,000 40,000... $53,217
(1 0.28) (1 0.28) (1 0.28)BS earnings
menPV
NPV = -15130
NPV = 3484
M&B_pv_college.xlsx
© 2013 Pearson Education, Inc. All rights reserved. 4-14
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
Interest Rates
P = price of bond when auctioned/issuedF = face value of bond c = annual coupon rate (in percent) C = dollar value of annual coupon payment = cFn = years to maturity date
coupon bond
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
© 2013 Pearson Education, Inc. All rights reserved. 4-15
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
10.0713.0713 .0713.0713 .071310
Interest Rates
coupon bond
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
© 2013 Pearson Education, Inc. All rights reserved. 4-16
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
10.0848.0848 .0848.0848 .084810
Interest Rates
coupon bond
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
© 2013 Pearson Education, Inc. All rights reserved. 4-17
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
10.1000.1000 .1000.1000 .100010
Interest Rates
coupon bond
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
© 2013 Pearson Education, Inc. All rights reserved. 4-18
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
10.1175.1175 .1175.1175 .117510
Interest Rates
coupon bond
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
© 2013 Pearson Education, Inc. All rights reserved. 4-19
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
10.1381.1381 .1381.1381 .138110
M&B_bond_prices.xlsx
Interest Rates
coupon bond
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
© 2013 Pearson Education, Inc. All rights reserved. 4-20
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
1010
Interest Rates
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
coupon bond
1200
© 2013 Pearson Education, Inc. All rights reserved. 4-21
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
1010
Interest Rates
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
coupon bond
1100
© 2013 Pearson Education, Inc. All rights reserved. 4-22
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
1010
Interest Rates
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
coupon bond
1000
© 2013 Pearson Education, Inc. All rights reserved. 4-23
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
1010
Interest Rates
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
coupon bond
900
© 2013 Pearson Education, Inc. All rights reserved. 4-24
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
c = 10%, n = 10, F = $1,000
1010
Interest Rates
M&B_yields.xlsx
100
100
100
100
1000
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
coupon bond
800
© 2013 Pearson Education, Inc. All rights reserved. 4-25
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
fixed payment loan
0
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
P = payment to borrower after loan is signedF = 0 C = annual cash payment n = years to maturity date
© 2013 Pearson Education, Inc. All rights reserved. 4-26
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
fixed payment loan
M&B_loan.xlsx
0
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
Example: You borrow $10,000 to buy a pickup. If you have to pay 60 monthly payments of $200, what is the interest rate? What is the annual rate of interest?
© 2013 Pearson Education, Inc. All rights reserved. 4-27
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
fixed payment loan
M&B_loan.xlsx
0
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
Example: You borrow $10,000 to buy a pickup. If you have to pay 60 monthly payments of $200, what is the interest rate? What is the annual rate of interest?
12 (1 ) 1i 0.006183413
© 2013 Pearson Education, Inc. All rights reserved. 4-28
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
fixed payment loan
M&B_loan.xlsx
0
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
Example: You borrow $10,000 to buy a pickup. If you have to pay 60 monthly payments of $200, what is the interest rate? What is the annual rate of interest?
7.68%i
© 2013 Pearson Education, Inc. All rights reserved. 4-29
Interest Rates
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
perpetuity (or consol) bond
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
© 2013 Pearson Education, Inc. All rights reserved. 4-30
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
perpetuity (or consol) bond
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-31
Interest Rates
perpetuity (or consol) bond
1 2 31/(1 ) 1/(1 ) 1/(1 ) i i i P
C
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-32
Interest Rates
perpetuity (or consol) bond
1 2 3x x x P
C
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-33
Interest Rates
0 1 2 31 x x x x P
C
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-34
Interest Rates
11
1
x
P
C
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-35
Interest Rates
1
x
x
P
C
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-36
Interest Rates
1/(1 )
1/(11 )i
i
P
C
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-37
Interest Rates
1/(1 )
/(1 )
i
i i
P
C
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-38
Interest Rates
1
i
P
C c
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-39
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
ci P
C
P = price of bond when auctioned/issuedF = 0 C = dollar value of annual coupon paymentn = infinity
© 2013 Pearson Education, Inc. All rights reserved. 4-40
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
Example: A consol pays out $20 annually, and interest rates are 5%. Compute the price of the consol.
ci P
C
© 2013 Pearson Education, Inc. All rights reserved. 4-41
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
Example: A consol pays out $20 annually, and interest rates are 5%. Compute the price of the consol.
.0520
P
© 2013 Pearson Education, Inc. All rights reserved. 4-42
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
Example: A consol pays out $20 annually, and interest rates are 5%. Compute the price of the consol.
P 20
.05
© 2013 Pearson Education, Inc. All rights reserved. 4-43
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
Example: A consol pays out $20 annually, and interest rates are 5%. Compute the price of the consol.
P 400
© 2013 Pearson Education, Inc. All rights reserved. 4-44
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
Example: A perpetuity that pays $150 annually is currently has a price of $2500. Compute the current yield of the perpetuity.
ciC
P
© 2013 Pearson Education, Inc. All rights reserved. 4-45
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
Example: A perpetuity that pays $150 annually is currently has a price of $2500. Compute the current yield of the perpetuity.
ci150
2500
© 2013 Pearson Education, Inc. All rights reserved. 4-46
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
Example: A perpetuity that pays $150 annually is currently has a price of $2500. Compute the current yield of the perpetuity.
ci .06
© 2013 Pearson Education, Inc. All rights reserved. 4-47
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
perpetuity (or consol) bond
Example: A perpetuity that pays $150 annually is currently has a price of $2500. Compute the current yield of the perpetuity.
ci 6%
© 2013 Pearson Education, Inc. All rights reserved. 4-48
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
Interest Rates
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
perpetuity (or consol) bond
Example: A perpetuity that pays $150 annually is currently has a price of $2500. Compute the current yield of the perpetuity using the above equation. To do this, assume the perpetuity ends in 5000 years and assume the future value is any value, say $1400. (Is 5000 years close to infinity? To the average human, yes.)
© 2013 Pearson Education, Inc. All rights reserved. 4-49
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
Interest Rates
2 3 3500 3500
14002500 . . .
1 (1 ) (1 ) (
150 150
1 ) (1 )
150 150
i i i i i
perpetuity (or consol) bond
Example: A perpetuity that pays $150 annually is currently has a price of $2500. Compute the current yield of the perpetuity using the above equation. To do this, assume the perpetuity ends in 3500 years and assume the future value is any value, say $1400. (Is 3500 years close to infinity? To the average human, yes.)
© 2013 Pearson Education, Inc. All rights reserved. 4-50
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
Interest Rates
perpetuity (or consol) bond
Example: A perpetuity that pays $150 annually is currently has a price of $2500. Compute the current yield of the perpetuity using the above equation. To do this, assume the perpetuity ends in 3500 years and assume the future value is any value, say $1400. (Is 3500 years close to infinity? To the average human, yes.)
ci 6%
M&B_perpetuity.xlsx
© 2013 Pearson Education, Inc. All rights reserved. 4-51
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
P = price of bond when auctioned/issuedF = face value of bond C = dollar value of annual coupon paymentn = years to maturity date
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
zero-coupon bond
© 2013 Pearson Education, Inc. All rights reserved. 4-52
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
P = price of bond when auctioned/issuedF = face value of bond C = 0n = years to maturity date
0 0 0 0
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
zero-coupon bond
© 2013 Pearson Education, Inc. All rights reserved. 4-53
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
P = price of bond when auctioned/issuedF = face value of bond n = years to maturity date
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
(1 )n
F
i
zero-coupon bond
© 2013 Pearson Education, Inc. All rights reserved. 4-54
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
P = price of bond when auctioned/issuedF = face value of bond n = years to maturity date
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
(1 )n
F
i
1/
1n
F
P
i
zero-coupon bond
© 2013 Pearson Education, Inc. All rights reserved. 4-55
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
(1 )n
F
i
1/
1n
F
P
i
zero-coupon bond
Example: Compute the interest rate on a $1000 bond that matures in nine years and costs $850 today.
© 2013 Pearson Education, Inc. All rights reserved. 4-56
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
1/
1n
F
P
i
zero-coupon bond
Example: Compute the interest rate on a $1000 bond that matures in nine years and costs $850 today.
© 2013 Pearson Education, Inc. All rights reserved. 4-57
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
1/91000
1850
i
zero-coupon bond
Example: Compute the interest rate on a $1000 bond that matures in nine years and costs $850 today.
© 2013 Pearson Education, Inc. All rights reserved. 4-58
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
.0182216842i
zero-coupon bond
Example: Compute the interest rate on a $1000 bond that matures in nine years and costs $850 today.
© 2013 Pearson Education, Inc. All rights reserved. 4-59
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
1.822%i
zero-coupon bond
Example: Compute the interest rate on a $1000 bond that matures in nine years and costs $850 today.
© 2013 Pearson Education, Inc. All rights reserved. 4-60
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
(1 )n
F
i
1/
1n
F
P
i
zero-coupon bond
Example: If you require a minimum of 5% on safe investments, what price are you willing to pay for a $1000 bond that matures in nine years?
© 2013 Pearson Education, Inc. All rights reserved. 4-61
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
(1 )n
F
i
zero-coupon bond
Example: If you require a minimum of 5% on safe investments, what price are you willing to pay for a $1000 bond that matures in nine years?
© 2013 Pearson Education, Inc. All rights reserved. 4-62
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
9
1000
(1 .05)
zero-coupon bond
Example: If you require a minimum of 5% on safe investments, what price are you willing to pay for a $1000 bond that matures in nine years?
© 2013 Pearson Education, Inc. All rights reserved. 4-63
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
$644.61
zero-coupon bond
Example: If you require a minimum of 5% on safe investments, what price are you willing to pay for a $1000 bond that matures in nine years?
© 2013 Pearson Education, Inc. All rights reserved. 4-64
Interest Rates
P = payment to borrower after the loan is signedC = cash payoff of loan’s principal and interest n = years to maturity date
simple loan
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i(1 )nC
i
1/
1n
P
iC
© 2013 Pearson Education, Inc. All rights reserved. 4-65
Interest Rates
simple loan
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i(1 )nC
i
1/
1n
P
iC
Example: If the annual interest rate is 10%, do you prefer $500 five years from now or $800 ten years from now?
The present value of getting $500 five years is The present value of getting $800 ten years is
© 2013 Pearson Education, Inc. All rights reserved. 4-66
Interest Rates
simple loan
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i5
5 0
(1
0
.10)
Example: If the annual interest rate is 10%, do you prefer $500 five years from now or $800 ten years from now?
The present value of getting $500 five years is The present value of getting $800 ten years is
© 2013 Pearson Education, Inc. All rights reserved. 4-67
Interest Rates
simple loan
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i310.46
Example: If the annual interest rate is 10%, do you prefer $500 five years from now or $800 ten years from now?
The present value of getting $500 five years is $310.46 The present value of getting $800 ten years is $308.43
© 2013 Pearson Education, Inc. All rights reserved. 4-68
Interest Rates
simple loan
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i10.11
80
( 0)
0
Example: If the annual interest rate is 10%, do you prefer $500 five years from now or $800 ten years from now?
The present value of getting $500 five years is $310.46 The present value of getting $800 ten years is $308.43
© 2013 Pearson Education, Inc. All rights reserved. 4-69
Interest Rates
simple loan
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Example: If the annual interest rate is 10%, do you prefer $500 five years from now or $800 ten years from now?
The present value of getting $500 five years is $310.46 The present value of getting $800 ten years is $308.43
308.43
© 2013 Pearson Education, Inc. All rights reserved. 4-70
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
P = price of bond when auctioned/issuedF = face value of bond n = 1 period
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
(1 )n
F
i
discount bond
© 2013 Pearson Education, Inc. All rights reserved. 4-71
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
P = price of bond when auctioned/issuedF = face value of bond n = 1 period
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
1(1 )
F
i
discount bond
© 2013 Pearson Education, Inc. All rights reserved. 4-72
Interest Rates
P = price of bond when auctioned/issuedF = face value of bond n = 1 period
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i1
F
i
© 2013 Pearson Education, Inc. All rights reserved. 4-73
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
P = price of bond when auctioned/issuedF = face value of bond n = 1 period
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
1
F
i 1
F
P i
© 2013 Pearson Education, Inc. All rights reserved. 4-74
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
1
F
i 1
F
P i
Example: Compute the interest rate on a $1000 bond that matures in one year and costs $850 today.
© 2013 Pearson Education, Inc. All rights reserved. 4-75
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
1F
P i
Example: Compute the interest rate on a $1000 bond that matures in one year and costs $850 today.
© 2013 Pearson Education, Inc. All rights reserved. 4-76
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
1000 1
850 i
Example: Compute the interest rate on a $1000 bond that matures in one year and costs $850 today.
© 2013 Pearson Education, Inc. All rights reserved. 4-77
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
.1764705882i
Example: Compute the interest rate on a $1000 bond that matures in one year and costs $850 today.
© 2013 Pearson Education, Inc. All rights reserved. 4-78
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
Example: Compute the interest rate on a $1000 bond that matures in one year and costs $850 today.
17.647%i
© 2013 Pearson Education, Inc. All rights reserved. 4-79
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
Example: What is the interest rate on a 10-year, $1000 bond that you purchased for $850 nine years after it was issued by the Treasury Department?
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i1
F
i 1
F
P i
© 2013 Pearson Education, Inc. All rights reserved. 4-80
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
1000 1
850 i
Example: What is the interest rate on a 10-year, $1000 bond that you purchased for $850 nine years after it was issued by the Treasury Department?
© 2013 Pearson Education, Inc. All rights reserved. 4-81
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
Example: What is the interest rate on a 10-year, $1000 bond that you purchased for $850 nine years after it was issued by the Treasury Department?
17.647%i
© 2013 Pearson Education, Inc. All rights reserved. 4-82
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
1
F
i 1
F
P i
Example: What price are you willing to pay for a $1000bond that matures in one year, if you require 5% interest?
© 2013 Pearson Education, Inc. All rights reserved. 4-83
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
1
F
i
Example: What price are you willing to pay for a $1000 bond that matures in one year, if you require 5% interest?
© 2013 Pearson Education, Inc. All rights reserved. 4-84
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
1000
1 .05
Example: What price are you willing to pay for a $1000 bond that matures in one year, if you require 5% interest?
© 2013 Pearson Education, Inc. All rights reserved. 4-85
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
discount bond
$952.38
Example: What price are you willing to pay for a $1000 bond that matures in one year, if you require 5% interest?
© 2013 Pearson Education, Inc. All rights reserved. 4-86
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
P = price of bond when auctioned/issuedC = cash payoff of loan’s principal and interestn = 1 period
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
1C
i 1
P i
C
simple loan
© 2013 Pearson Education, Inc. All rights reserved. 4-87
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
1C
i 1
P i
C
Example: If you borrow $200 and you agree to pay the lender $205 at the end of the month, what is the monthly interest rate? What is the annual interest rate?
simple loan
© 2013 Pearson Education, Inc. All rights reserved. 4-88
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
1P
iC
simple loan
Example: If you borrow $200 and you agree to pay the lender $205 at the end of the month, what is the monthly interest rate? What is the annual interest rate?
© 2013 Pearson Education, Inc. All rights reserved. 4-89
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
205 1
200 i
simple loan
Example: If you borrow $200 and you agree to pay the lender $205 at the end of the month, what is the monthly interest rate? What is the annual interest rate?
© 2013 Pearson Education, Inc. All rights reserved. 4-90
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
5% 2.i
simple loan
Example: If you borrow $200 and you agree to pay the lender $205 at the end of the month, what is the monthly interest rate? What is the annual interest rate?
© 2013 Pearson Education, Inc. All rights reserved. 4-91
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
simple loan
12.025 (1 ) 1 i
Example: If you borrow $200 and you agree to pay the lender $205 at the end of the month, what is the monthly interest rate? What is the annual interest rate?
5% 2.i
© 2013 Pearson Education, Inc. All rights reserved. 4-92
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
simple loan
.3448888242i
Example: If you borrow $200 and you agree to pay the lender $205 at the end of the month, what is the monthly interest rate? What is the annual interest rate?
5% 2.i
© 2013 Pearson Education, Inc. All rights reserved. 4-93
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
simple loan
Example: If you borrow $200 and you agree to pay the lender $205 at the end of the month, what is the monthly interest rate? What is the annual interest rate?
5% 2.i
34.489%i
© 2013 Pearson Education, Inc. All rights reserved. 4-94
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
1C
i 1
P i
C
Example: If your mom lends you $200 and you agree to pay her $250 when you get paid at the end of the month, what is the monthly interest rate? What is the annual interest rate?
simple loan
© 2013 Pearson Education, Inc. All rights reserved. 4-95
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
1P
iC
Example: If your mom lends you $200 and you agree to pay her $250 when you get paid at the end of the month, what is the monthly interest rate? What is the annual interest rate?
simple loan
© 2013 Pearson Education, Inc. All rights reserved. 4-96
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
250 1
200 i
simple loan
Example: If your mom lends you $200 and you agree to pay her $250 when you get paid at the end of the month, what is the monthly interest rate? What is the annual interest rate?
© 2013 Pearson Education, Inc. All rights reserved. 4-97
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
5% 2i
simple loan
Example: If your mom lends you $200 and you agree to pay her $250 when you get paid at the end of the month, what is the monthly interest rate? What is the annual interest rate?
© 2013 Pearson Education, Inc. All rights reserved. 4-98
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
simple loan
12.2 (1 )5 1 i
5% 2i
Example: If your mom lends you $200 and you agree to pay her $250 when you get paid at the end of the month, what is the monthly interest rate? What is the annual interest rate?
© 2013 Pearson Education, Inc. All rights reserved. 4-99
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
simple loan
13.55191523i
5% 2i
Example: If your mom lends you $200 and you agree to pay her $250 when you get paid at the end of the month, what is the monthly interest rate? What is the annual interest rate?
© 2013 Pearson Education, Inc. All rights reserved. 4-100
Interest Rates
In Money & Banking, the discount rate is
• market rate of interest i on a loan:
• called the Yield to Maturity
simple loan
1355.192%i
5% 2i
Example: If your mom lends you $200 and you agree to pay her $250 when you get paid at the end of the month, what is the monthly interest rate? What is the annual interest rate?
© 2013 Pearson Education, Inc. All rights reserved. 4-101
1. The price of a bond falls
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
as interest rates rise.
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-102
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
2 3 . . .
1 (1 ) (1 ) (1 ) (1 )n n
FP
C C
i
C
i i i
C
i
as interest rates rise.
no Interest-Rate Risk
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-103
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is purchased and held for its final year,
1 1
FP
R R
C
as interest rates rise.
i i
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-104
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is purchased and held for its final year,
1
FP
R
C
as interest rates rise.
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-105
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is purchased and held for its final year,
as interest rates rise.
1F
RP
C
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-106
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is purchased and held for its final year,
1F
RP
C
as interest rates rise.
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-107
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is purchased and held for its final year,
as interest rates rise.
F PR
P
C
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-108
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is purchased and held for its final year,
as interest rates rise.
F PR
P P
C
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-109
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a zero-coupon bond is purchased and held for its final year,
as interest rates rise.
Bond Properties
0 F PR
P P
© 2013 Pearson Education, Inc. All rights reserved. 4-110
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a zero-coupon bond is purchased and held for its final year,
as interest rates rise.
F PR
P
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-111
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is purchased and held for its final year, and its
purchase price equals its face value,
F PR
P P
C
as interest rates rise.
F
F
F
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-112
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is purchased and held for its final year, and its
purchase price equals its face value,
FR
F
c F
as interest rates rise.
F c
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-113
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is held for one year and sold before it matures,
as interest rates rise.
F PR
P P
C t
tt
Pt+1ci g
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-114
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a zero-coupon bond is held for one year and sold before it matures,
as interest rates rise.
F PR
P P
C t
tt
Pt+1g
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-115
1. The price of a bond falls
2. The rate of return (R) is the return on a bond held for a given period of time
• R = yield to maturity only if it is held for all n periods
• R ≠ yield to maturity if the bond is held less than n periodso If a coupon bond is held for one year, and sold before it matures for the
same price it was purchased,
as interest rates rise.
F PR
P P
Cci
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-116
3. A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period
4. The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change
5. The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate
6. Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-117
3. A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period
4. The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change
5. The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate
6. Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise
2 3 4 5 5
1 (1 ) (1 ) (1 ) (1 ) (1 )
FP
C C C
i i i i i i
C C
.10
100
100
100
100
1000
100
.10 .10 .10 .10 .10= 1000
c = 10%, n = 5, F = $1,000
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-118
= 1000
3. A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period
4. The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change
5. The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate
6. Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise
2 3 4 5 5
1 (1 ) (1 ) (1 ) (1 ) (1 )
FP
C C C
i i i i i i
C C
c = 10%, n = 5, F = $1,000
.20 .20 .20 .20 .20 .20= 741
100
100
100
100
1000
100
M&B_bond_properties.xlsx
Bond Properties
© 2013 Pearson Education, Inc. All rights reserved. 4-119
3. A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period
4. The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change
5. The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate
6. Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise
7. Prices and returns for long-term bonds are more volatile than those for shorter-term bonds
Interest-Rate Risk
Bond Properties