Lecture 5 Geometric Gradient Series, Finishing Chapter 2

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Lecture 5Geometric Gradient Series, Finishing
Chapter 2

• Read 84-102
• Problems 2.30, 32, 35, 38, 39, 47, 52
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• Do the self-test in studying for Exam.

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Geometric Gradient

• Increasing/decreasing at a constant percentage,
  not a constant amount
• g gt 0, series will increase, g lt 0, series will
  decrease

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A
A(1g)N-1
A(1-g)
A(1g)
A
A(1-g)N-1
Or
P
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Present Worth Pn, of any cash flow An, at i is
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Then subtract the two equations from one another
as we did in our earlier derivations.
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Geometric gradient series present worth factor
(P/A,g,i,N)

• Unlike the linear gradient the annual amount is
  imbedded in the equation.

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Example

• Airplane ticket price will increase 8 in each of
  the next four years. The cost at the end of the
  first year will be 180. How much should be put
  away now to cover a students travel home at the
  end of each year for the next four years? Assume
  5.

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• As a check we can also solve this problem without
  using the geometric gradient
• Year Ticket
• 1 A1 180
• 2 A2 180 8(180) 194.40
• 3 A3 194.40 8 (194.50) 209.95
• 4 A4 209.95 8 (209.95) 226.75
• P 180(P/F,5,1) 194.40(P/F,5,2)
  209.95(P/F,5,3) 226.75(P/F,5,4)
• 715.66
• There are no tables for the geometric gradient.

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Future worth FactorSince F P(1i)Multiplying
(P/A,g,i,n) by (1i) will give F 
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Example

• A graduating CE is going to make 35,000/yr with
  Granite Construction. A total of 10 of the CE
  salary will be placed in the mutual fund of their
  choice. The CE can count on a 3 salary
  increase with the standard of living increases
  for the next 30 years of employment. If the CE
  is aggressive and places their retirement in a
  stock index fund that will average 12 over the
  course of their career, what can the CE expect at
  retirement?

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A 35,000 x 0.1 3,500i 12g 3n 30
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• Recall that all of the interest equations can
  only be used when interest period is the same as
  the compounding period.

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Problem 2.15 revisitedMany of you solved this
problem using brute force,

• P 1,000,000 800,000(P/F,8,1) .
  1,000,000(P/F,8,10) 6,911,539
• You should just recognize that you could also
  solve it by
• P 1,000,000 800,000(P/A,8,5)
  1,000,000(P/A,8,5)(P/F,8,5)

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Or

• P 1,000,000 100,000(P/A,8,10)
  200,000(P/A,8,5)
• Recognizing multiple ways to solve a problem will
  be crucial on the exam!
• More Complicated Example,
• Solve the following Cash Flow diagram for Present
  Worth,

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• Chapter 2 is now complete. All of the basic
  equations have been presented.
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• Most of the basic equations are functions on the
  spread sheet programs like excel, lotus, and
  there is a downloadable program made by the
  author of the textbook