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Unformatted text preview: 61CHAPTER 5Time Value of MoneyFuture valuePresent valueAnnuitiesRates of returnAmortizationNote: Slides have been slightly revised from those provided by the publisher.62Time linesShow the timing of cash flows (timing of cash flows is important because a dollar in year 1 has a higher value than a dollar in year 2).Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.CFCF1CF3CF2123i%63Drawing time lines:$100 lump sum due in 2 years;3year $100 ordinary annuity100100100123i%3 year $100 ordinary annuity10012i%$100 lump sum due in 2 years64Drawing time lines:Uneven cash flow stream; CF = $50, CF1 = $100, CF2 = $75, and CF3 = $50 1005075123i%50Uneven cash flow stream65What is the future value (FV) of an initial $100 after 3 years, if I/YR = 10%?Example: How much will you have in 3 years if you deposit $100 today into a banking account that pays 10% per year?The FV is equivalent to the amount of money you will have in your banking account in 3 yearsFinding the FV of a cash flow or series of cash flows when compound interest is applied is called compounding.FV can be solved by using the arithmetic, financial calculator, and spreadsheet methods.FV = ?12310%10066Solving for FV:The arithmetic methodAfter 1 year:FV1 = Principal + Interest = Principal + Principal * Interest Rate = Principal * (1+ Interest Rate) = PV ( 1 + i ) = $100 (1.1) = $110.00After 2 years:FV2 = ( Principal + Interest Rate) * ( 1 + i ) = PV ( 1 + i )2 = $100 (1.10)2 =$121.00After 3 years:FV3 = PV ( 1 + i )3 = $100 (1.10)3 =$133.10After n years (the general case):FVn = PV ( 1 + i )n67Solving for FV:The arithmetic methodMathematically, a $100 deposited for three years will be growing to $133.10 in three years.FV = PV * (1 + Interest Rate)3 = PV ( 1 + i )3 = $100 (1.10)3 =$133.10Alternatively,FV = PV (FVIFi, N) = $100 (FVIF10%, 3) = $100 * 1.3310 = $133.1068Solving for FV:The arithmetic methodThe mathematical formula for the FV: FVN = PV*(1+i)NEquivalently: FVN = PV* (FVIFi, N)so FV Interest Factor = (FVIFi, N) = (1+i)N69Solving for FV:The calculator methodSolves the general FV equation....
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This note was uploaded on 11/11/2011 for the course FIN 350 taught by Professor Chen during the Spring '07 term at S.F. State.
 Spring '07
 Chen
 Finance

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