Chapter 6Time Value of MoneySimple InterestCompound InterestSlide 5Slide 6Future Value of a Single AmountSlide 8Slide 9Slide 10Slide 11Slide 12Slide 13Present Value of a Single AmountSlide 15Slide 16Slide 17Slide 18Slide 19Time Value of Money ExampleSlide 21Slide 22Slide 23Present ValueSlide 25Slide 26Solving for Other ValuesSolving for Other Variables ExampleSlide 29No Explicit InterestExpected Cash Flow ApproachBasic AnnuitiesOrdinary AnnuityAnnuity DueFuture Value of an Ordinary AnnuitySlide 36Slide 37Slide 38Future Value of an Annuity DueSlide 40Present Value of an Ordinary AnnuitySlide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Present Value of an Annuity DueSlide 52Present Value of AnnuitiesSlide 54Present Value of a Deferred AnnuitySlide 56Slide 57End of Chapter 6© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinChapter 6Time Value of Money Concepts© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-2Time Value of MoneyInterest is therent paid for the useof money over time.That’s right! A dollartoday is more valuablethan a dollar to bereceived in one year.© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-3Simple InterestInterest amount = P × i × nAssume you invest $1,000 at 6% simple interest for 3 years.You would earn $180 interest.($1,000 × .06 × 3 = $180)(or $60 each year for 3 years)© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-4Compound InterestWhen we compound interest, we assume you earn interest on both principal and interest.Principal Interest© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-5 Assume we will save $1,000 for three years and earn 6% interest compounded annually.What is the balance inour account at theend of three years?Compound Interest© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-6Compound Interest© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-7Future Value of a Single AmountMultiply a year’s beginning principal by the interest rate and add that year’s interest to the account balance.$1,000.00 × 1.06 = $1,060.00and$1,060.00 × 1.06 = $1,123.60and$1,123.60 × 1.06 = $1,191.02© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-8Writing in a more efficient way, we can say . . . .$1,000 × 1.06 × 1.06 × 1.06 = $1,191.02or$1,000 × [1.06]3 = $1,191.02Future Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-9$1,000 × [1.06]3 = $1,191.02We can generalize this as . . .FV = PV (1 + i)nFutureValueFutureValuePresentValuePresentValueInterestRateInterestRateNumberof PeriodsNumberof PeriodsFuture Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-10 Find the Future Value of $1 table in your textbook. Future Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-11Find the factor for 6% and 3 periods.Solve our problem like this. . .FV = $1,000.00 × 1.19102FV = $1,191.02FV $1Future Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-12You invest $10,000 today and earn 8% interest for 8 years. What will the balance in your account be at the end of 8 years if . . . .A. Interest is simple.B. Interest is compounded annually.Future Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-13A - Simple InterestA - Simple Interest$10,000 × .08 × 8 = $6,400$10,000 + $6,400 = $16,400A - Simple InterestA - Simple Interest$10,000 × .08 × 8 = $6,400$10,000 + $6,400 = $16,400B - Compound AnnuallyB - Compound Annually$10,000 × 1.85093 = $18,509.30B - Compound AnnuallyB - Compound Annually$10,000 × 1.85093 = $18,509.30Future Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-14Instead of asking what is the future value of a current amount, we might want to know what amount we must invest today to accumulate a known future amount.This is a present value question.Present Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-15Remember our equation?FV = PV [1 + i]nWe can solve for PV and get . . . . FV [1 + i]nPV =Present Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-16We can rearrange the equation . . .oror [1 + i]-nPV = FVPresent Value of a Single Amount 1 [1 + i]nPV = FV© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-17 Find the Present Value of $1 table in your textbook. Hey, it looks familiar!Present Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-18Assume you plan to buy a new car in 5 years and you think it will cost $20,000 at that time.What amount must you invest today in order to accumulate $20,000 in 5 years, if you can earn 8% interest compounded annually?Present Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-19i = .08, n = 5Present Value Factor = .68058$20,000 × .68058 = $13,611.60If you deposit $13,611.60 now, at 8% annual interest, you will have $20,000 at the end of 5 years.Present Value of a Single Amount© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-20Time Value of Money Example If you deposit $5,000 in a bank at 8% interest compounded annually, how much will you have in 5 years? . . . in 10 years?5 Years 10 Yearsa. $7,387 $8,144b. $7,347 $10,795c. $7,347 $9,471d. $6,984 $9,186© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-21 If you deposit $5,000 in a bank at 8% interest compounded annually, how much will you have in 5 years? . . . in 10 years?5 Years 10 Yearsa. $7,387 $8,144b. $7,347 $10,795c. $7,347 $9,471d. $6,984 $9,186Future Value of $1 Table$5,000 × 1.46933 = $ 7,346.65$5,000 × 2.15892 = $10,794.60Time Value of Money Example© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-22 What amount must you deposit today at 6% interest compounded annually, to have $10,000 for your first year of college 5 years from now?a. $7,462b. $7,921c. $7,473d. $7,581Time Value of Money Example© 2004 The McGraw-Hill Companies, Inc.McGraw-Hill/IrwinSlide6-23 What amount must you deposit today at 6% interest compounded annually, to have $10,000 for your first year of college 5 years from now?a. $7,462b. $7,921c. $7,473d. $7,581Present Value of $1 Table$10,000 x .74726 = $7,472.60Time Value of Money Example© 2004 The McGraw-Hill