Isues in economics today 6th by guell chapter07
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Chapter 07
Interest
Rates and
Present
Value
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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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