1. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. Chapter 4 Interest Rates and Present Value

2. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. Chapter Outline Interest Rates Present Value

3. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest Rates The Market for Money

4. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

5. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. Figure 1 The Market for Money Supply Demand r* $* Interest rate (r) Money ($) Borrowed/Saved

6. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

7. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

8. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. The Amount Payable for Every Dollar Borrowed (For several interest rates and loan durations) Interest rate -> Years  20%10%5%2%1% 30237.3817.454.321.811.35 106.192.591.631.221.10 52.491.611.281.101.05 11.201.101.051.021.01

9. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

10. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

11. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. A Multiple Year Example Suppose you pay $100 for the first 5 years then receive $100 for the next 7 years. The present value of the can be depicted in the picture below. For instance the present value of the $100 paid in the fifth year is $100/(1.10) 4 or $68.30.

12. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. Monthly Payments Required on per $1000 of loan (For Several Interest Rates and Loan Durations) Interest rate -> Years  20%10%5%2%1% 3016.718.785.373.703.22 1019.3313.2210.619.208.76 526.4921.2518.8717.5317.09 192.6387.9285.6184.2483.79

13. McGraw-Hill/Irwin © 2002 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.