Chapter 3Learning Objectives3.1 Future Value and the Compounding of Interest3.1 (A) The Single-Period Scenario3.1 (B) The Multiple-Period Scenario3.1 (C) Methods of Solving Future Value Problems3.1 (C) Methods of Solving Future Value Problems (continued)3.1 (C) Methods of Solving Future Value Problems (continued)3.1 (C) Methods of Solving Future Value Problems (Continued)Slide 113.2 Present Value and Discounting3.2 (A) The Single-Period Scenario3.2 (B) The Multiple-Period Scenario3.2 Present Value and Discounting (continued)Slide 16Slide 173.2 (C) Using Time LinesPowerPoint Presentation3.3 One Equation, Four Variables3.4 Applications of the TVM Equation: A Present Value ProblemSlide 223.4 Application of the TVM Equation: A Present Value Problem (continued)3.4 Application of the TVM Equation: A Future Value Problem3.4 Application of the TVM Equation: A Future Value Problem (continued)Slide 263.4 Application of the TVM Equation: An Interest Rate Problem3.4 Application of the TVM Equation: An Interest Rate Problem (continued)Slide 293.4 Application of the TVM Equation: A Growth Rate Problem3.4 Application of the TVM Equation: A Growth Rate Problem (continued)Slide 323.4 Application of the TVM Equation: A Waiting Time Problem3.4 Application of the TVM Equation: A Waiting Time Problem (continued)Slide 35ADDITIONAL PROBLEMS WITH ANSWERS Problem 1ADDITIONAL PROBLEMS WITH ANSWERS Problem 1 (ANSWER)ADDITIONAL PROBLEMS WITH ANSWERS Problem 1 (ANSWER) (continued)ADDITIONAL PROBLEMS WITH ANSWERS Problem 2ADDITIONAL PROBLEMS WITH ANSWERS Problem 2 (ANSWER)ADDITIONAL PROBLEMS WITH ANSWERS Problem 2 (ANSWER continued)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)ADDITIONAL PROBLEMS WITH ANSWERS Problem 5ADDITIONAL PROBLEMS WITH ANSWERS Problem 5 (ANSWER)Table 3.1 Annual Interest Rates at 10% for $100 Initial Deposit (Rounded to Nearest Penny)TABLE 3.2 Variable Match for Calculator and SpreadsheetTABLE 3.3 Doubling Time in Years for Given Interest RatesCopyright © 2010 Pearson Prentice Hall. All rights reserved.Chapter 3The Time Value of Money (Part 1)Copyright © 2010 Pearson Prentice Hall. All rights reserved.3-2Learning Objectives1. Calculate future values and understand compounding.2. Calculate present values and understand discounting.3. Calculate implied interest rates and waiting time from the time value of money equation. 4. Apply the time value of money equation using formula, calculator, and spreadsheet.5. Explain the Rule of 72, a simple estimation of doubling values.Copyright © 2010 Pearson Prentice Hall. All rights reserved.3-33.1 Future Value and the Compounding of Interest•Future value is the value of an asset in the future that is equivalent in value to a specific amount today. –Compound interest is interest earned on interest.–These concepts help us to determine the attractiveness of alternative investments. –They also help us to figure out the effect of inflation on the future cost of assets, such as a car or a house.Copyright © 2010 Pearson Prentice Hall. All rights reserved.3-43.1 (A) The Single-Period Scenario FV = PV + PV x interest rate, or FV = PV(1+interest rate) (in decimals)Example 1: Let’s say John deposits $200 for a year in an account that pays 6% per year. At the end of the year, he will have:?FV = $200 + ($200 x .06) = $212 = $200(1.06) = $212?Copyright © 2010 Pearson Prentice Hall. All rights reserved.3-53.1 (B) The Multiple-Period ScenarioFV = PV x (1+r)nExample 2: If John closes out his account after 3 years, how much money will he have accumulated? How much of that is the interest-on-interest component? What about after 10 years??FV3 = $200(1.06)3 = $200*1.191016 = $238.20,where 6% interest per year for 3 years = $200 x.06 x 3=$36Interest on interest = $238.20 - $200 - $36 =$2.20FV10 = $200(1.06)10 = $200 x 1.790847 = $358.17where 6% interest per year for 10 years = $200 x .06 x 10 = $120Interest on interest = $358.17 - $200 - $120 = $38.17Copyright © 2010 Pearson Prentice Hall. All rights reserved.3-63.1 (C) Methods of Solving Future Value Problems•Method 1: The formula method –Time-consuming, tedious, but least dependent•Method 2: The financial calculator approach –Quick and easy•Method 3: The spreadsheet method–Most versatile•Method 4: The use of time value tables: –Easy and convenient, but most limiting in scopeCopyright © 2010 Pearson Prentice Hall. All rights reserved.3-73.1 (C) Methods of Solving Future Value Problems (continued) Example 3: Compounding of Interest?Let’s say you want to know how much money you will have accumulated in your bank account after 4 years, if you deposit all $5,000 of your high-school graduation gifts into an account that pays a fixed interest rate of 5% per year. You leave the money untouched for all four of your college years.Copyright © 2010 Pearson Prentice Hall. All rights reserved.3-83.1 (C) Methods of Solving Future Value Problems (continued)Example 3: AnswerFormula Method:FV = PV x (1+r)n$5,000(1.05)4=$6,077.53Calculator method: PV =-5,000; N=4; I/Y=5; PMT=0; CPT FV=$6077.53Spreadsheet method:Rate = .05; Nper = 4; Pmt=0; PV=-5,000; Type =0; FV=6077.53Time value table method:FV = PV(FVIF, 5%, 4) = 5000*(1.215506)=6077.53, where (FVIF, 5%,4) = Future value interest factor listed under the 5% column and in the 4-year row of the Future Value of $1 table.Copyright © 2010 Pearson Prentice Hall. All rights reserved.3-9Example 4: Future Cost due to InflationLet’s say that you have seen your dream house, which is currently listed at $300,000, but unfortunately, you are not in a position to buy it right away and will have to wait at least another 5 years before you will be able to afford it. If house values are appreciating at the average annual rate of inflation of 5%, how much will a similar house cost after 5 years?3.1 (C) Methods of Solving Future Value Problems (continued)Copyright © 2010 Pearson Prentice Hall. All rights reserved.3-103.1 (C) Methods of Solving Future Value Problems (Continued)Example 4 (Answer)PV = current cost of the house = $300,000n = 5 yearsr = average annual inflation rate = 5%Solving for FV, we have?FV = $300,000*(1.05)(1.05)(1.05)(1.05)(1.05) = $300,000*(1.276282) = $382,884.5?So the house will cost $382,884.5 after 5