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Isues in economics today 6th by guell chapter07

Chapter 07
Interest
Rates and
Present
Value

McGraw-Hill/Irwin

Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.


Chapter Outline
• Interest Rates
• Present Value
• Future Value
• Kick It Up a Notch: Risk and Reward

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Interest Rates
The Market for Money

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Interest Rate
• The interest rate is the percentage,
usually expressed in annual terms, of a
balance that is paid by a borrower to a
lender that is in addition to the original
amount borrowed or lent.

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Figure 1 The Market for Money
Interest
rate (r)

Supply

r*

Demand
$*


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Money ($)
Borrowed/Saved

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Nominal vs. Real Interest Rates
• Nominal Interest Rate: the advertised rate
of interest
• Real Interest Rate: the rate of interest after
inflation expectations are accounted for; the
compensation for waiting on consumption

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Present Value
• Present Value is the interest adjusted value of
future payment streams.
• Mathematically, the present value of a payment
is

=(payment)/(1+r)n
Where
r is the interest rate
n is the number of years until the
payment is received/made.

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The Amount Payable for Every Dollar
Borrowed (For several interest rates
and loan durations)
Interest
rate ->
Years ↓

30

20% 10%

5%

2%

1%

10

237. 17.4 4.32 1.81 1.35
38
5
6.19 2.59 1.63 1.22 1.10

5

2.49 1.61 1.28 1.10 1.05

1

1.20 1.10 1.05 1.02 1.01

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Examples From This Table
• If you borrow $1 and promise to pay it back in
5 years at 5% interest you will owe $1.28
which is the original $1 plus 28 cents in
interest.
• If you borrow $1 and promise to pay it back in
30 years at 20% interest you will owe $237.38
which is the original $1 plus $236.38 in
interest.

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Mortgages, Car Payments,
and other Multiple-Payment Examples
• Mortgages are loans taken out to buy homes.
Typically you borrow a large sum of money
and promise to pay it back in even amounts
each month for 10, 15, or 30 years.
• Car loans are similar to mortgages in that
you borrow a large sum but the loan duration
is usually two to six years.

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A Multiple Year Example @ 5%
Year

Cost

Benefit

PV Cost
@5%

1

100

100.00

2

100

95.24

3

100

90.70

4

100

86.38

5

100

82.27

PV Benefit
@5%

6

100

78.35

7

100

74.62

8

100

71.07

9

100

67.68

10

100

64.46

11

100

61.39

12

100

58.47

500
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700

454.60

476.05

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A Multiple Year Example @ 8%
Year

Cost

PV Cost
@8%

Benefit

1

100

100.00

2

100

92.59

3

100

85.73

4

100

79.38

5

100

73.50

PV Benefit
@8%

6

100

68.06

7

100

63.02

8

100

58.35

9

100

54.03

10

100

50.02

11

100

46.32

12

100

42.89

500
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700

431.21

382.68

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A Multiple Year Example @ 10%
Year

Cost

PV Cost
@10%

Benefit

1

100

100.00

2

100

90.91

3

100

82.64

4

100

75.13

5

100

68.30

PV Benefit
@10%

6

100

62.09

7

100

56.45

8

100

51.32

9

100

46.65

10

100

42.41

11

100

38.55

12

100

35.05

500
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700

416.99

332.52

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Internal rate of return
• Internal rate of return : The interest rate
where the present value of costs and
benefits are equal.

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Monthly Payments Required on per
$1000 of loan (For Several Interest
Rates and Loan Durations)
Intere
st
rate
->
Years


20%

10%

5%

2%

1%

30

16.7
1
19.3
3

8.78

5.37

3.70

3.22

13.2
2

10.6
1

9.20

8.76

10

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Examples From This Table
• If you borrow $1000 and promise to pay it
back monthly over 5 years at 5% interest
you will owe $18.87 per month.
• If you borrow $1000 and promise to pay it
back monthly over 10 years at 20% interest
you will owe $19.33 per month.

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Future Value
• Future value: the interest-adjusted value of past
payments.

Future Value = payment × (1 + r )

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Rule of 72
• Rule of 72: A short cut that allows you
to estimate the time it would take for an
investment to double by dividing 72 by
the annual interest rate.
• For example: How long would it take to
double your money ($10,000) at 4%
interest?
• FV formula: $10,000x(1.04)^18=$20,258.17 (so
a little less than 18 years is the answer).
• Rule of 72: 72/4=18 years

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Kick It Up A Notch:
Risk and Reward

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Kick It Up A Notch: Risk and
Reward
• Risk: the possibility that the investor will not
get those anticipated payoffs
• Default Risk: the risk to the investor that
the borrower will not pay
• Market Risk: the risk that the market value
of an asset will change in an unanticipated
manner
• Reward
• Risk Premium the reward investors
receive for taking greater risk
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The Yield Curve
• Yield Curve: the relationship between reward and
the time until the reward is received

US Treasury Yield Curve (January 2005)

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