Chapter 2 - FALL 2010

Chapter 2 - FALL 2010 - CHAPTER 2 The Value of a Single...

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CHAPTER 2 The Value of a Single Payment Now Compared to a Single Payment in the Future P/F “P given F” F/P “F given P”

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CHAPTER OUTLINE Cash Flow Diagrams Concept of “Equivalence” P/F or F/P Meaning: Find “ P ” given “ F ” or Find “ F given “ P Finding the present value given the future value Finding the future value given the present value Discrete Compounding equations on page 36 Solving for P, F, i, and n Understanding and manipulating interest rates
The Flow of Cash in any transaction can be represented in a “Cash Flow Diagram” This diagram shows a present worth “ P P ” of an amount of money and a future worth “ F F ”of that amount over a period of time “ n n ” determined by an interest rate “ i i applied to the original amount. CASH FLOW DIAGRAMS i i =Interest Rate Present Worth ( P P ) n n = Number of Payment periods Future Value (F) Future Value (F)

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The concept of equivalence is central to Engineering Economy The term “Equivalence” means that an amount of money today P P ” differs from some later sum “ F F ”or series amount “A” only by the amount of accrued interest at a stated interest rate i i accumulated during the intervening n n compounding periods. For example: You want to purchase a new car that costs “ P P You could pay “ P P ” now and owe nothing more on the car, or You could finance the car monthly over 5 years at some interest rate i i and you would pay 60 payments whose total would be much greater than “ P P The total of this series of payments however, is considered to be equivalent (over time) to “ P P ” …. .why? Because if instead of buying the car you had invested your money, “ P P ” in some investment paying you an interest rate of i you would have the same amount of money that you would have spent on financing the car. EQUIVALENCE
To see how equivalence works, let’s look at the examples shown in Figures 2.3 through 2.6 Figures 2.3 through 2.6 2.3 – Plan A Plan A - Payment of interest only 2.4 – Plan B Plan B – Repay equal amounts of principle each time. 2.5 – Plan C Plan C – Equal annual payments. 2.6 – Plan D Plan D – Lump sum payment at the end. EQUIVALENCE

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DISCRETE COMPOUNDING EQUATIONS Page 36 n i P F ) 1 ( + = ( 29 ) 1 ln( ln i P F n + = ( 29 1 1 - = n P F i n i F P ) 1 ( + = Definitions P = Present Worth F = Future Worth i = Interest Rate n = # of periods
SOLVING PROBLEMS Two Methods 1. Formulas (page 36) 2. Functional Notation “Short Cut” Instead of formulas we may use interest rate tables (found in the back of the book). F = P (F/P, i, n)

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This note was uploaded on 02/07/2011 for the course CGN 4101 taught by Professor Wise during the Spring '08 term at University of Florida.

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Chapter 2 - FALL 2010 - CHAPTER 2 The Value of a Single...

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