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Chapter 6 Spring 2010 (white)

Chapter 6 Spring 2010 (white) - CHAPTER 6 Geometric...

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CHAPTER 6 Geometric Gradients: The Constant Percentage Increment
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HW Chapter 6 Due Thursday 2/11/10 Chapter 6 B.7 B.8 C.6 C.7 C.12 D.1
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Geometric versus Arithmetic Geometric Gradients increase by a constant percentage. “Maintenance increases at 10% per year CH 5, Arithmetic Gradients increased by a constant amount Maintenance increases $500 per year” CH 5 Gradients could be broken down into an “A” and a “G”
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Geometric Gradients CAN NOT be broken down into an A and a G The percentage the gradient increases or decreases is constant but the amount will vary We use “ C C ” – the first payment in the series and “ r r the rate of increase of the gradient If you read the words “increase” or “decrease” you should think gradient If you see a % associated with the increase or decrease you should think Geometric Gradient Geometric Gradients CAN NOT be broken into and “A” and a “G”
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Cash Flow Diagrams C C C(1+r) C(1+r) 0 0 1 1 2 2 3 3 4 4 5 5 P is found 1 period prior to C - You can only solve directly for “P” Equation Time 0 is 1 PERIOD prior to C C(1+r) C(1+r) 2 2 C(1+r) C(1+r) 3 3 C(1+r) C(1+r) 4 4 10,000 10,000 11,000 11,000 12,100 12,100 13,310 13,310 14,641 14,641 Note that C is not increasing by a constant amount
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Cash Flow Diagrams 0 0 1 1 2 2 3 3 4 4 5 5 6 6 C = 10,000 r = 10% i = ?
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Equations – front cover – Three Cases - + + = w w i C P n 1 ) 1 ( 1 CASE 1 CASE 1 r > i - + + = 1 1 1 i r w The rate of increase of the gradient is greater than the interest rate
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Equations – front cover CASE 2 CASE 2 r < i The rate of increase of the gradient is smaller than the interest rate + - + + = n n w w w r C P ) 1 ( 1 ) 1 ( 1 - + + = 1 1 1 r i w
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Equations – front cover CASE 3 CASE 3 r = i The rate of increase of the gradient is equal to the interest rate i Cn r Cn P + = + = 1 1
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Equations – Special Case n n ° r ( 29 w r C P + = 1 1 P is always found 1 PERIOD prior to the first C C = the initial payment in the gradient (p. 137) You must keep 5 significant digits for w - If not you will introduce excessive error
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