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# Topic 2_1_student - Topic 2 The Time Value of Money...

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Unformatted text preview: Topic 2 The Time Value of Money Readings: Chap 4 (4.1-4.4) Introduction to the time value of money Choice between \$100 and \$110 right now Which one do you prefer? Choice between \$100 today and \$110 in 1 year. Which one do you prefer? Introduction to the time value of money Many business and personal decisions involve a trade-off of cash flows between points in time. For example We need the tools of interest rate mathematics to compare bundles or streams of cash flows over time. Single Cash Flow What is Present Value (PV) and Future Value (FV)? ( 1 ) 1 ( 1 ) n n F V P V r P V F V r = + = + n is the n umber of years r is the annual r ate of interest FV is value in n years (F uture V alue) PV is value today (P resent V alue) Future Value - single sums If you deposit \$100 in an account earning 6%, how much would you have in the account after 1 year? FV = PV (1 + i) n FV = 100 (1.06) 1 = \$106 1 1 PV = -100 PV = -100 FV = FV = 106 106 Example - Compound Interest Suppose you put \$100 in a savings account that earns a 6% interest compounded annually. Today Future Years 1 2 3 4 5 Interest Earned Balance 100 Future Values 6 106 6.36 112.36 6.74 119.10 7.15 126.25 7.57 133.82 Compounding: A Famous Example Peter Minuit bought Manhattan for \$24 in 1624: (383 years ago) In 2007 @ 5% \$24 (1.05)^383 =\$3,131,214,255 In 2007 @ 10% \$24 (1.10)^383 =\$1.712 x 10^17 In 2007 @ 15% \$24 (1.15)^383 =\$4.241 x 10^24 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% Future Values with Compounding Interest Rates Choice between \$100 today and \$110 in 1 year...
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## This note was uploaded on 06/07/2011 for the course FINANCE 103 taught by Professor None during the Spring '11 term at University of Illinois, Urbana Champaign.

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Topic 2_1_student - Topic 2 The Time Value of Money...

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