# Chapter 5 - CHAPTER 5 Time Value of Money Topics Covered...

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CHAPTER 5 Time Value of Money

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Topics Covered Time lines Future Values and Compound Interest Present Values Multiple Cash Flows Level Cash Flows Perpetuities and Annuities Effective Annual Interest Rates Inflation & Time Value
Time lines Show the timing of cash flows. 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. CF 0 CF 1 CF 3 CF 2 0 1 2 3 I%

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Drawing time lines 100 100 100 0 1 2 3 I=5% 3 year \$100 ordinary annuity FV=? 0 1 2 I=5% \$100 lump sum due in 2 years PV=\$100 PV=?
Drawing time lines 100  50  75 0 1 2 3 I=? -50 Uneven cash flow stream

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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.
Future Values Example - Simple Interest Interest earned at a rate of 6% for five years on a principal balance of \$100. Interest Earned Per Year = 100 x .06 = \$ 6

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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 Future Values 6 106 6 112 6 118 6 124 6 130 Value at the end of Year 5 = \$130
Future Values Example - Compound Interest Interest earned at a rate of 6% for five years on the previous year’s balance. Interest Earned Per Year = Prior Year Balance x .06

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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 Future Values 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
Future Values Future Value of \$100 = FV FV r t = × + \$100 ( ) 1

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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
Solving for FV: The calculator method Solves the general FV equation. Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.) INPUTS OUTPUT N I/YR PMT PV FV 5 6 0 133.82 -100

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0 200 400 600 800 1000 1200 1400 1600 1800 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of Years FV of \$100 0% 5% 10% 15% Future Values with Compounding Interest Rates
Present Values Present Value = PV PV = Future Value after t periods (1+r) t

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Chapter 5 - CHAPTER 5 Time Value of Money Topics Covered...

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