Chapter 7 Interest Rates and Present Value Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

7-2 Chapter Outline Interest Rates Present Value

7-3 You Are Here

7-4 Interest Rates The Market for Money

7-5 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.

7-6 Figure 1 The Market for Money Supply Demand r* $* Interest rate (r) Money ($) Borrowed/Saved

7-7 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

7-8 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.

7-9 The Amount Payable for Every Dollar Borrowed (For several interest rates and loan durations) Interest rate -> Years  20%10%5%2%1%

7-10 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.

7-11 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.

7-12 A Multiple Year 5% YearCostBenefitPV

7-13 A Multiple Year 8% YearCostBenefitPV

7-14 A Multiple Year 10% YearCostBenefitPV

7-15 Internal rate of return Internal rate of return : The interest rate where the present value of costs and benefits are equal.

7-16 Monthly Payments Required on per $1000 of loan (For Several Interest Rates and Loan Durations) Interest rate -> Years  20%10%5%2%1%

7-17 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.

7-18 Future Value Future value: the interest-adjusted value of past payments.

7-19 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, (so a little less than 18 years is the answer). Rule of 72: 72/4=18 years

7-20 Kick It Up A Notch: Risk and Reward

7-21 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

7-22 The Yield Curve Yield Curve: the relationship between reward and the time until the reward is received US Treasury Yield Curve (January 2005)