Slide 1CHAPTER OUTLINEInterest RatesInterest RateFigure 1 The Market for MoneyNominal vs. Real Interest RatesPresent ValueSlide 8Examples From This TableMortgages, Car Payments, and other Multiple-Payment ExamplesSlide 11Examples From This TableMulti-Year AnalysisA Multiple Year Example @ 5%A Multiple Year Example @ 8%A Multiple Year Example @ 10%Internal Rate of ReturnFuture ValueRule of 72Kick It Up A Notch: Risk and RewardThe Yield Curve7-1©2015 McGraw-Hill Education. All Rights Reserved ©2015 McGraw-Hill Education. All Rights Reserved Chapter 7 Interest Rates and Present Value7-2©2015 McGraw-Hill Education. All Rights Reserved CHAPTER OUTLINE•Interest Rates•Present Value•Future Value•Kick It Up a Notch: Risk and Reward7-3©2015 McGraw-Hill Education. All Rights Reserved Interest RatesThe Market for Money7-4©2015 McGraw-Hill Education. 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.7-5©2015 McGraw-Hill Education. All Rights Reserved Figure 1 The Market for MoneySupplyDemandr*$*Interest rate (r) Money ($) Borrowed/Saved7-6©2015 McGraw-Hill Education. 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 consumption7-7©2015 McGraw-Hill Education. 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 raten is the number of years until the payment is received/made.7-8©2015 McGraw-Hill Education. 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%30 237.3817.454.32 1.81 1.3510 6.19 2.59 1.63 1.22 1.105 2.49 1.61 1.28 1.10 1.051 1.20 1.10 1.05 1.02 1.017-9©2015 McGraw-Hill Education. 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.7-10©2015 McGraw-Hill Education. 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.7-11©2015 McGraw-Hill Education. 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%30 16.718.78 5.37 3.70 3.2210 19.3313.2210.619.20 8.765 26.4921.2518.8717.5317.091 92.6387.9285.6184.2483.797-12©2015 McGraw-Hill Education. 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.7-13©2015 McGraw-Hill Education. All Rights Reserved Multi-Year Analysis•Many investments garner upfront costs and yield later benefits.•The wisdom of these investments depends on whether the present value of benefits is greater than the present value of costs.•The present value of the same cash flows depends greatly on the interest rate.7-14©2015 McGraw-Hill Education. All Rights Reserved A Multiple Year Example @ 5%Year Cost Benefit PV Cost @5% PV Benefit @5%1 100 100.002 100 95.243 100 90.704 100 86.385 100 82.276 100 78.357 100 74.628 100 71.079 100 67.6810 100 64.4611 100 61.3912 100 58.47500 700 454.60 476.057-15©2015 McGraw-Hill Education. All Rights Reserved A Multiple Year Example @ 8%Year Cost Benefit PV Cost @8%PV Benefit @8%1 100 100.002 100 92.593 100 85.734 100 79.385 100 73.506 100 68.067 100 63.028 100 58.359 100 54.0310 100 50.0211 100 46.3212 100 42.89500 700 431.21 382.687-16©2015 McGraw-Hill Education. All Rights Reserved A Multiple Year Example @ 10%Year Cost Benefit PV Cost @10%PV Benefit @10%1 100 100.002 100 90.913 100 82.644 100 75.135 100 68.306 100 62.097 100 56.458 100 51.329 100 46.6510 100 42.4111 100 38.5512 100 35.05500 700 416.99 332.527-17©2015 McGraw-Hill Education. All Rights Reserved Internal Rate of Return•Internal rate of return : The interest rate where the present value of costs and benefits are equal.7-18©2015 McGraw-Hill Education. All Rights Reserved Future Value•Future value: the interest-adjusted value of past payments. nrpaymentValueFuture  17-19©2015 McGraw-Hill Education. All Rights Reserved 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 years7-20©2015 McGraw-Hill Education. All Rights Reserved 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 risk7-21©2015 McGraw-Hill Education. All Rights Reserved The Yield Curve•Yield Curve: the relationship between reward and the time until the reward is receivedU.S. Treasury Yield Curve (January