1. Chapter 7 Interest Rates and Present Value
Issues In Economics Today, 4e
Guell
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Chapter Outline
Interest Rates
Present Value

3. You Are Here

4. Interest Rates
The Market for Money

5. 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.

6. Figure 1 The Market for Money
Interest rate (r)
Money ($) Borrowed/Saved
Supply
Demand r* $*

7. 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

8. 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.

9. Interest rate -> Years 
The Amount Payable for Every Dollar Borrowed (For several interest rates and loan durations)
Interest rate -> Years 
20%
10% 5% 2% 1% 30
237.38
17.45
4.32
1.81
1.35 10
6.19
2.59
1.63
1.22
1.10 5
2.49
1.61
1.28
1.05 1
1.20
1.02
1.01

10. 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 $ which is the original $1 plus $ in interest.

11. 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.

12. A Multiple Year Example @ 5%
Cost
Benefit PV PV 1
100
100.00 2
95.24 3
90.70 4
86.38 5
82.27 6
78.35 7
74.62 8
71.07 9
67.68 10
64.46 11
61.39 12
58.47
500
700
454.60
476.05

13. A Multiple Year Example @ 8%
Cost
Benefit PV PV 1
100
100.00 2
92.59 3
85.73 4
79.38 5
73.50 6
68.06 7
63.02 8
58.35 9
54.03 10
50.02 11
46.32 12
42.89
500
700
431.21
382.68

14. A Multiple Year Example @ 10%
Cost
Benefit PV PV 1
100
100.00 2
90.91 3
82.64 4
75.13 5
68.30 6
62.09 7
56.45 8
51.32 9
46.65 10
42.41 11
38.55 12
35.05
500
700
416.99
332.52

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

16. Interest rate -> Years 
Monthly Payments Required on per $1000 of loan (For Several Interest Rates and Loan Durations)
Interest rate -> Years 
20%
10% 5% 2% 1% 30
16.71
8.78
5.37
3.70
3.22 10
19.33
13.22
10.61
9.20
8.76 5
26.49
21.25
18.87
17.53
17.09 1
92.63
87.92
85.61
84.24
83.79

17. 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.

18. Kick It Up A Notch:
Risk and Reward

19. 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

20. The Yield Curve
Yield Curve: the relationship between reward and the time until the reward is received
US Treasury Yield Curve (January 2005)