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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**The Market for Money**Interest Rates**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.**Interest rate (r)**Supply r* Demand Money ($) Borrowed/Saved $* Figure 1 The Market for Money**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**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.**The Amount Payable for Every Dollar Borrowed (For several**interest rates and loan durations)**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.**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.**Internal rate of return**• Internal rate of return : The interest rate where the present value of costs and benefits are equal.**Monthly Payments Required on per $1000 of loan (For Several**Interest Rates and Loan Durations)**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.**Future Value**• Future value: the interest-adjusted value of past payments.**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**Risk and Reward**Kick It Up A Notch:**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**The Yield Curve**• Yield Curve:the relationship between reward and the time until the reward is received US Treasury Yield Curve (January 2005)