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**Unformatted text preview: **1 Chapter 5 The Time Value of Money Some Important Concepts 2 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rates. Inflation 3 Future Values Future Value- Amount to which an investment will grow after earning interest. Compound Interest- Interest earned on interest. Simple Interest- Interest earned only on the original investment. 4 Future Values Example - Simple Interest Interest earned at a rate of 6% for five years on a principal balance of $100. Today Future Years 1 2 3 4 5 Interest Earned Value 100 6 106 6 112 6 118 6 124 6 130 Value at the end of Year 5 = $130 5 Future Values Example - Compound Interest Interest earned at a rate of 6% for five years on the previous year’s balance . Today Future Years 1 2 3 4 5 Interest Earned Value 100 6 106 6.36 112.36 6.74 119.10 7.15 126.25 7.57 133.82 Value at the end of Year 5 = $133.82 6 Future Values Future Value of $100 = FV FV r t = × + $100 ( ) 1 7 Future Values FV r t = × + $100 ( ) 1 Example - FV What is the future value of $100 if interest is compounded annually at a rate of 6% for five years? 82 . 133 $ ) 06 . 1 ( 100 $ 5 = + × = FV Financial calculator: n=5, i=6, PV=-100, PMT=0 FV= 133.82 8 Future Values 1000 2000 3000 4000 5000 6000 7000 2 4 6 8 1 1 2 1 4 1 6 1 8 2 2 2 2 4 2 6 2 8 3 Number of Years FV of $100 0% 5% 10% 15% 9 Future Values Example – Manhattan Island Sale Peter Minuit bought Manhattan Island for $24 in 1626. Was this a good deal? trillion FV 57 . 120 $ ) 08 . 1 ( 24 $ 380 = + × = To answer, determine $24 is worth in the year 2006, compounded at 8%. Financial calculator: n=380, i=8, PV=-24, PMT=0 FV= $120.57 trillion 10 Present Values If you are offered the choice between $100,000 now and $100,000 at the end of the year, which one would you choose? Present value : Value today of a future cash flow. 11 Present Values If the interest rate is at 6 percent per year, how much do we need to invest now in order to produce $106 at the end of the year? How much would we need to invest now to produce $112.36 after two years? 100 $ 06 . 1 106 $ 1.06 value future (PV) lue Present va = = = 100 $ 06 . 1 36 . 112 $ 1.06 value future (PV) lue Present va 2 2 = = = 12 Present Values t r) + (1 periods after t Value Future = PV Discount Factor (DF) = PV of $1 Discount Factors can be used to compute the present value of any cash flow....

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