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

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