Chapter 44.1 Future Value of Multiple Payment StreamsFIGURE 4.1 The time line of a nest egg4.1 Future Value of Multiple Payment Streams (continued)4.1 Future Value of Multiple Payment Streams (Example 1 Answer)4.2 Future Value of an Annuity Stream4.2 Future Value of an Annuity Stream (continued)Slide 9Slide 104.2 Future Value of an Annuity Stream (continued)FIGURE 4.3 Interest and principal growth with different interest rates for $100-annual payments.4.3 Present Value of an AnnuityFIGURE 4.4 Time line of present value of annuity stream.4.3 Present Value of an Annuity (continued)4.3 Present Value of an Annuity (continued)Slide 17Slide 184.4 Annuity Due and PerpetuitySlide 204.4 Annuity Due and Perpetuity (continued)Slide 22Slide 23Slide 244.5 Three Payment Methods4.5 Three Payment Methods (continued)Slide 27Slide 28Slide 294.6 Amortization Schedules4.6 Amortization Schedules (continued)Slide 324.7 Waiting Time and Interest Rates for Annuities4.7 Waiting Time and Interest Rates for Annuities (continued)Slide 354.8 Solving a Lottery Problem4.8 Solving a Lottery Problem (continued)Slide 384.9 Ten Important Points about the TVM Equation4.9 Ten Important Points about the TVM Equation (continued)Slide 41ADDITIONAL PROBLEMS WITH ANSWERS Problem 1ADDITIONAL PROBLEMS WITH ANSWERS Problem 1 (ANSWER)ADDITIONAL PROBLEMS WITH ANSWERS Problem 2ADDITIONAL PROBLEMS WITH ANSWERS Problem 2 (ANSWER)ADDITIONAL PROBLEMS WITH ANSWERS Problem 3ADDITIONAL PROBLEMS WITH ANSWERS Problem 3 (ANSWER)ADDITIONAL PROBLEMS WITH ANSWERS Problem 4ADDITIONAL PROBLEMS WITH ANSWERS Problem 4 (ANSWER)ADDITIONAL PROBLEMS WITH ANSWERS Problem 4 (ANSWER continued)Slide 51ADDITIONAL PROBLEMS WITH ANSWERS Problem 4 (ANSWER continued)ADDITIONAL PROBLEMS WITH ANSWERS Problem 5ADDITIONAL PROBLEMS WITH ANSWERS Problem 5 (ANSWER)Slide 55Slide 56Slide 57Copyright © 2010 Pearson Prentice Hall. All rights reserved.Chapter 4The Time Value of Money (Part 2)Copyright © 2010 Pearson Prentice Hall. All rights reserved.4-21. Compute the future value of multiple cash flows.2. Determine the future value of an annuity.3. Determine the present value of an annuity.4. Adjust the annuity formula for present value and future value for an annuity due, and understand the concept of a perpetuity. 5. Distinguish between the different types of loan repayments: discount loans, interest-only loans, and amortized loans.6. Build and analyze amortization schedules.7. Calculate waiting time and interest rates for an annuity.Learning ObjectivesCopyright © 2010 Pearson Prentice Hall. All rights reserved.4-34.1 Future Value of Multiple Payment Streams•With unequal periodic cash flows, treat each of the cash flows as a lump sum and calculate its future value over the relevant number of periods. •Sum up the individual future values to get the future value of the multiple payment streams.Copyright © 2010 Pearson Prentice Hall. All rights reserved.4-4FIGURE 4.1 The time line of a nest eggCopyright © 2010 Pearson Prentice Hall. All rights reserved.4-54.1 Future Value of Multiple Payment Streams (continued)Example 1: Future Value of an Uneven Cash Flow StreamJim deposits $3,000 today into an account that pays 10% per year, and follows it up with 3 more deposits at the end of each of the next three years. Each subsequent deposit is $2,000 higher than the previous one. How much money will Jim have accumulated in his account by the end of three years?Copyright © 2010 Pearson Prentice Hall. All rights reserved.4-64.1 Future Value of Multiple Payment Streams (Example 1 Answer)FV = PV x (1+r)nFV of Cash Flow at T0 = $3,000 x (1.10)3 = $3,000 x 1.331= $3,993.00FV of Cash Flow at T1 = $5,000 x (1.10)2 = $5,000 x 1.210 = $6,050.00FV of Cash Flow at T2 = $7,000 x (1.10)1 = $7,000 x 1.100 = $7,700.00FV of Cash Flow at T3 = $9,000 x (1.10)0 = $9,000 x 1.000 = $9,000.00 Total = $26,743.00Copyright © 2010 Pearson Prentice Hall. All rights reserved.4-74.2 Future Value of an Annuity StreamCopyright © 2010 Pearson Prentice Hall. All rights reserved.4-84.2 Future Value of an Annuity Stream (continued)Example 2: Future Value of an Ordinary Annuity StreamJill has been faithfully depositing $2,000 at the end of each year for the past 10 years into an account that pays 8% per year. How much money will she have accumulated in the account?Copyright © 2010 Pearson Prentice Hall. All rights reserved.4-9Example 2 AnswerFuture Value of Payment One = $2,000 x 1.089 = $3,998.01Future Value of Payment Two = $2,000 x 1.088 = $3,701.86Future Value of Payment Three = $2,000 x 1.087 = $3,427.65Future Value of Payment Four = $2,000 x 1.086 = $3,173.75 Future Value of Payment Five = $2,000 x 1.085 = $2,938.66 Future Value of Payment Six = $2,000 x 1.084 = $2,720.98 Future Value of Payment Seven = $2,000 x 1.083 = $2,519.42 Future Value of Payment Eight = $2,000 x 1.082 = $2,332.80 Future Value of Payment Nine = $2,000 x 1.081 = $2,160.00 Future Value of Payment Ten = $2,000 x 1.080 = $2,000.00Total Value of Account at the end of 10 years $28,973.134.2 Future Value of an Annuity Stream (continued)Copyright © 2010 Pearson Prentice Hall. All rights reserved.4-104.2 Future Value of an Annuity Stream (continued)Copyright © 2010 Pearson Prentice Hall. All rights reserved.4-114.2 Future Value of an Annuity Stream (continued) USING AN EXCEL SPREADSHEET EEnter =FV(8%, 10, -2000, 0, 0); Output = $28,973.13Enter =FV(8%, 10, -2000, 0, 0); Output = $28,973.13 Rate, Nper, Pmt, PV,TypeType is 0 for ordinary annuities and 1 for annuities due.USING FVIFA TABLE (Appendix 3 in text)Find the FVIFA in the 8% column and the 10 period row: FVIFA FVIFA = 14.486= 14.486FV = 2000*14.4865 = $28.973.13FV = 2000*14.4865 = $28.973.13Copyright © 2010 Pearson Prentice Hall. All rights reserved.4-12FIGURE 4.3 Interest and principal growth with different interest rates for $100-annual payments.Copyright © 2010 Pearson Prentice Hall. All rights reserved.4-134.3 Present Value of an Annuity PV PMT 1 11  r nrTo calculate the value of a series of equal periodic cash flows at the current point in time, we can use the following simplified formula: The last portion of the equation is the Present Value Interest Factor of an Annuity (PVIFA). Practical applications include figuring out the nest egg needed prior to retirement or the lump sum needed for college expenses.Copyright © 2010 Pearson Prentice Hall. All rights