Chapter 4 -Spring 2010 (white)

# Chapter 4 -Spring 2010 (white) - CHAPTER 4 The Value of one...

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CHAPTER 4 The Value of one present payment compared to a uniform series of payments P/A “P given A” A/P “A given P”

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HW # 3 3 Due Thursday 01/28/10 Chapter 4 A.2 A.4 B.1 B.2 C.4 D.9
CHAPTER OUTLINE Meaning “ A given P or P given A Finding the annual value given the Present value Finding the Present value given the annual value The Present value of periodic payments Solving for A , P , i , and n

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Additional Information Definitions A = Uniform Series P = Present Worth i = Interest Rate n = # of periods Uses Finding the present worth of a series of payments Finding the equivalent payments that result from a present lump sum “If I want monthly payments of \$X when I retire how much do I have to save” Functional Notation P = A (P/A, i, n) A = P (A/P, i, n)
Equations ( 29 ( 29 + - + = n n i i i A P 1 1 1 ( 29 i A Pi n + - = 1 ln 1 1 ln n i A P 1 =

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Cash Flow Diagrams 0 1 2 3 4 5 6 7 8 9 10 11 n P A A A A A A A A A A A A A A A A A A A A A A A A
MY Cash Flow Diagrams 0 1 2 3 4 5 6 7 8 9 10 11 n P A = A = i =

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Cash Flow Diagrams 0 1 2 3 4 5 6 7 8 9 10 11 n p A A A A A A A A A A A A P occurs 1 PERIOD prior to the first A A transaction occurs at time = n
Example Cash Flow Diagrams P 0 1 2 3 4 5 6 7 8 9 10 11 12 A A A A A A P occurs 1 PERIOD, in this case 2 months, prior to the first A 1 0 2 3 4 5 6

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Cash Flow Diagrams P 0 1 2 3 4 5 6 7 8 9 10 11 12 A A A A A A P occurs 1 PERIOD prior to the first A, in this case that happens to be at t = -1 -1 1 0 2 3 4 5 6 This P must be moved to t = 0
Shifting Cash Flow Diagrams The scale (n’s) on cash flow diagrams are shifted whenever the problem cash flow does not look like the front cover of the book When we are asked for P it is always meant at t = 0 When we solve for P is is always found 1 PERIOD prior to the first A regardless of where t = 0.

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Chapter 4 -Spring 2010 (white) - CHAPTER 4 The Value of one...

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