IOE+201+Notes+4

# IOE+201+Notes+4 - IOE 201 Lecture Notes 4 Geometric...

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1 0 1 2 3 4 5 6 7 8 P Geometric Gradient Series of Payments A 1 Interest Periods i = Interest rate per period g = Percentage change per period N = Number of interest periods (e.g., N = 8) A 1 (1+ g ) 8 7 1 4 3 1 3 2 1 2 1 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( i g A i g A i g A i g A i A + + + + + + + + + + + + + + 3 2 7 6 Present worth P = IOE 201 Lecture Notes 4

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2 Geometric Gradient Series of Payments: Formula for General N where i g c + + = 1 1 N N i g A i g A i g A i g A i A P ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 1 4 3 1 3 2 1 2 1 1 + + + + + + + + + + + + + + = - + + + + + + + + + + + + + + = - - 1 1 3 3 2 2 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 ) 1 ( N N i g i g i g i g i A { } 1 3 2 1 1 ) 1 ( - + + + + + + = N c c c c i A - - + = c c i A N 1 1 ) 1 ( 1 if c 1 (i.e., i g ) + - + + - + = - - 1 1 ) 1 ( ) ( ) 1 ( ) 1 ( 1 ) 1 ( i g i i g i A N N - + + - = - ) ( ) 1 ( ) 1 ( 1 1 g i i g A N N (sum of geometric progression)
3 Geometric Gradient Series of Payments: Formula for General N where i g c + + = 1 1 { } 1 3 2 1 1 ) 1 ( - + + + + + + = N c c c c i A P ( 29 N i A ) 1 ( 1 + = if i g + - + + - = - i N A g i i g A P N N 1 ) ( ) 1 ( ) 1 ( 1 1 1 ( 29 1 1 1 1 1 ) 1 ( 1 + + + + + + = i A if c = 1 (i.e., i = g ) For case i = g : For all i and g : if i = g Present worth

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## This note was uploaded on 03/17/2010 for the course IOE 201 taught by Professor Dennisblumenfield during the Fall '09 term at University of Michigan-Dearborn.

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IOE+201+Notes+4 - IOE 201 Lecture Notes 4 Geometric...

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