Chapter 6 Fall 2010

Chapter 6 Fall 2010 - CHAPTER 6 Geometric Gradients: The...

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CHAPTER 6 Geometric Gradients: The Constant Percentage Increment
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HW Chapter 6 Due Tuesday 9/28/10 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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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 There are only equations to solve for There are only equations to solve for P, so if you need anything else, (such P, so if you need anything else, (such as A or F) you must first find P. as A or F) you must first find P.
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Chapter 6 Fall 2010 - CHAPTER 6 Geometric Gradients: The...

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