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Lecture 5 Geometric Gradient Series, Finishing Chapter 2

Lecture 5 Geometric Gradient Series, Finishing Chapter 2. Read 84-102 Problems 2.30, 32, 35, 38, 39, 47, 52 Do the self-test in studying for Exam. Geometric Gradient. Increasing/decreasing at a constant percentage, not a constant amount

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Lecture 5 Geometric Gradient Series, Finishing Chapter 2

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  1. Lecture 5Geometric Gradient Series, Finishing Chapter 2 Read 84-102 Problems 2.30, 32, 35, 38, 39, 47, 52 Do the self-test in studying for Exam.

  2. Geometric Gradient • Increasing/decreasing at a constant percentage, not a constant amount • g > 0, series will increase, g < 0, series will decrease

  3. A A(1+g)N-1 A(1-g) A(1+g) A A(1-g)N-1 Or P

  4. Present Worth Pn, of any cash flow An, at i is:

  5. Then subtract the two equations from one another as we did in our earlier derivations.

  6. Geometric gradient series present worth factor (P/A,g,i,N) Unlike the linear gradient the annual amount is imbedded in the equation.

  7. 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%.

  8. 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.

  9. Future worth FactorSince F =P(1+i)Multiplying (P/A,g,i,n) by (1+i) will give F

  10. 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?

  11. A = 35,000 x 0.1 = 3,500i = 12%g = 3%n = 30

  12. Recall that all of the interest equations can only be used when interest period is the same as the compounding period.

  13. 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)

  14. 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,

  15. Chapter 2 is now complete. All of the basic equations have been presented. • 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

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