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ISYE 3025 Engineering Economics - Week 2

by: Moriah Mattson

ISYE 3025 Engineering Economics - Week 2 ISYE 3025

Marketplace > Georgia Institute of Technology > Industrial Engineering > ISYE 3025 > ISYE 3025 Engineering Economics Week 2
Moriah Mattson
Georgia Tech
GPA 3.67

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About this Document

These notes cover the last three videos in Learning Cycle 1: Equivalence Formulas Part 1, Equivalence Formulas Part 2, and Interest Rate Conversions.
Engineering Economy
Kelly Bartlett
Class Notes
Engineering, Economics
25 ?




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This 8 page Class Notes was uploaded by Moriah Mattson on Thursday September 1, 2016. The Class Notes belongs to ISYE 3025 at Georgia Institute of Technology taught by Kelly Bartlett in Fall 2016. Since its upload, it has received 9 views. For similar materials see Engineering Economy in Industrial Engineering at Georgia Institute of Technology.

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Date Created: 09/01/16
  ISYE Engineering Economics ­ Week 2    Video ­ Equivalence Formulas  Purpose: To become familiar with four classic equivalence models and their associated  formulas    Conventions​­> In this class, the end­of­period model will be used. This means that the  amount is assumed to be accumulated or paid by the ​end​ of the time frame.      Model 1: Single Cash Flow    This model involves a single payment, which is then analyzed at a later period of time.                      The general formula to find the Final amount from a Payment is…  F = P(1 + i)​  =  P(F/P,i,N) ​<­ The part in the parenthesis is read as “Finding F given P   with an interest rate of i, compounded over a period of N” This value can be looked up  in the Appendix with this notation. You can also find an equivalent P for a value at F  with the formula…    P = F(1 + i)​  = F(P/F,i,N)                        Model 2: Uniform Cash Flow    This model shows a series of equal payments (A) over a certain period of time.    The general formula to find the Final amount from this cash flow model is…  Before Simplification: ​F = A(1 + i)​ N­1 + A(1 + i)​ N­2+ … + A(1 + i) + A  After Simplification: ​F = A [(1 + i)​  ­ 1] / i = A(F/A,i,N)      The general formula to find the payment amount (A) from a Final amount over a period  of time is…  A = Fi / [(1 + i)​  ­ 1] = F(A/F,i,N)        The general formula to find the equivalent Payment (P) to a cash flow (A) so they have  the same Final amount…  N​ N​ P = A [((1 + i)​  ­ 1) / i(1 + i)​ ] = A(P/A,i,N)      The general formula to find an equivalent cash flow (A) to a one time Payment (P)...  A = P [i(1 + i)​  / ((1 + i)​  ­ 1)] = P(A/P.i.N)      Model 3: Arithmetic Gradient Series    This model shows a series of payments that increase linearly over a period of time.      The general formula to find an equivalent one time Payment (P) to the linearly  increasing payments (G) is…  P = G [((1 + i)​  ­ iN ­ 1) / (i​ (1 + i)​ ] = G(P/G,i,N)      The general formula to find an equivalent uniform cash flow (A) for a arithmetic gradient  series (G) is…  A = G [((1 + i)​  ­ iN ­ 1) / (i(1 + i)​  ­ i)] = G(A/G,i,N)                      Model 4: Geometric Gradient Series    This model shows a series of payments that increase by a given percentage (g) each  year. The shape of the series changes as g changes.             The general formula for finding an equivalent one time Payment (P) to a geometric  gradient series (A​ ) that increased at a specified rate (g) is…  1​ P = {A​ [(11​ (1 + g)​  (1 + i)​ ) / (i ­ g)] for ​i does not g  ­1​        {A​ 1​1 + i)​  for ​i equals g  P = A​ (P1​​ ,i,g,1​                    Video ­ Interest Rate Conversions     Time scale conversions are essentially a unit change from one time measurement to  another.    M2/M1​ Formula:​ ​i​M1​ (1 + i​ M2​  ­ 1    Nominal Annual Interest Rate:​ The stated interest rate without taking any fees or  compounding interest into account   Rate, r = Mi​  M   Effective Annual Interest Rate:​ The actual interest rate that is associated with an  investment due to compounding over a period of time  i = (1 + i​M​​  ­ 1 ​where i should include all costs and M = number of months in  period 


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