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1、The Time Value of Money4In order to work the problems in this module, the user should have the use of a business calculator such as the Hewlett Packard 17BII.4The author grants individuals a limited license to use this presentation. It is the sole property of the author who holds the corresponding c
2、opyrights. The user agrees not to reproduce, duplicate or distribute any copies of this presentation in any form.4The author would like to thank the Innovative Technology Center at The University of Tennessee which supported this project with a grant through the “Teaching with Technology Summer Inst
3、itute.” She would also like to commend the teachers who helped her design the module.4If you have any comments or suggestions on how to improve this presentation, please e-mail the author at smurphyutk.edu. Copyright 2000 Suzan Murphy4In order to work the problems in this module, the user should hav
4、e the use of a business calculator such as the Hewlett Packard 17BII.4The author grants individuals a limited license to use this presentation. It is the sole property of the author who holds the corresponding copyrights. The user agrees not to reproduce, duplicate or distribute any copies of this p
5、resentation in any form.4The author would like to thank the Innovative Technology Center at The University of Tennessee which supported this project with a grant through the “Teaching with Technology Summer Institute.” She would also like to commend the teachers who helped her design the module.4If
6、you have any comments or suggestions on how to improve this presentation, please e-mail the author at smurphyutk.edu. Copyright 2000 Suzan MurphyThe Time Value of Money4What is the “Time Value of Money”?4 Compound Interest4 Future Value4 Present Value4 Frequency of Compounding4 Annuities4 Multiple C
7、ash Flows4 Bond ValuationObviously, $1,000 today$1,000 today.Money received sooner rather than later allows one to use the funds for investment or consumption purposes. This concept is referred to as the TIME VALUE OF MONEYTIME VALUE OF MONEY!The Time Value of MoneyWhich would you rather have - $1,0
8、00 today $1,000 today or $1,000 in 5 years?$1,000 in 5 years? TIME TIME allows one the opportunity to postpone consumption and earn INTERESTINTEREST. NOT having the opportunity to earn interest on money is called OPPORTUNITY COST. Why TIME?How can one compare amounts in different time periods?4One c
9、an adjust values from different time periods using an interest rate.4Remember, one CANNOT compare numbers in different time periods without first adjusting them using an interest rate.Compound InterestWhen interest is paid on not only the principal amount invested, but also on any previous interest
10、earned, this is called compound interest.FV = Principal + (Principal x Interest) = 2000 + (2000 x .06)= 2000 (1 + i)= PV (1 + i)Note: PV refers to Present Value or PrincipalIf you invested $2,000 today in an account $2,000 today in an account that pays 6that pays 6% interest, with interest compounde
11、d annually, how much will be in the account at the end of two years if there are no withdrawals?Future Value (Graphic)0 1 2 $2,000$2,000FVFV6%FV FV1 1= PVPV (1+i)n = $2,000$2,000 (1.06)2 = $2,247.20$2,247.20Future Value (Formula)FV = future value, a value at some future point in time PV = present va
12、lue, a value today which is usually designated as time 0 i = rate of interest per compounding period n = number of compounding periodsCalculator Keystrokes: 1.06 (2nd yx) 2 x 2000 =Future Value (HP 17 B II Calculator)262000 +/-NI%YrPV2,247.20FVExit until you get Fin Menu. 2nd, Clear Data. Choose Fin
13、, then TVMJohn wants to know how large his $5,000$5,000 deposit will become at an annual compound interest rate of 8% at the end of 5 years5 years.Future Value Example0 1 2 3 4 5 5$5,000$5,000FVFV5 58%4Calculator keystrokes: 1.08 2nd yx x 5000 =Future Value SolutionuCalculation based on general form
14、ula: FVFVn n= PV (1+i)n FVFV5 5= $5,000 (1+ 0.08)5= $7,346.64$7,346.64Future Value (HP 17 B II Calculator)85000 +/-FVNI%YrPV7,346.64Exit until you get Fin Menu. 2nd, Clear Data. Choose Fin, then TVM5Double Your Money!Quick! How long does it take to double $5,000 at a compound rate of 12% per year (a
15、pprox.)?We will use the “ “Rule-of-72Rule-of-72” ”. .The “Rule-of-72”Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)?Approx. Years to Double = 7272 / i%72 72 / 12% = 6 Years6 Years Actual Time is 6.12 YearsPresent Value4Since FV = PV(1 + i)n.PVPV = FVFV / (
16、1+i)n.4Discounting is the process of translating a future value or a set of future cash flows into a present value.Assume that you need to have exactly $4,000$4,000 saved 10 years from now. years from now. How much must you deposit today in an account that pays 6% interest, compounded annually, so that you reach your goal of $4,000?0 5 5 10$4,000$4,0006%PVPV0 0Present Value (Graphic)PVPV0 0= FVFV / (1+i)2 = $4,0
