1. Interest Formulas (Gradient Series)
Lecture No.8
Chapter 3
Contemporary Engineering Economics
Copyright © 2010
Contemporary Engineering Economics, 5th edition, © 2010

2. Linear Gradient Series
A Strict Gradient Series
Gradient Series as a Composite Series of a Uniform Series of N Payments of A1 and the Gradient Series of Increments of Constant Amount G.
Contemporary Engineering Economics, 5th edition, © 2010

3. Example3.21 Linear Gradient: Find P, Given A1, G, N, and i
Given: A1 = $1,000, G = $250, N = 5 years, and i = 12% per year
Find: P
Excel Solution:
Contemporary Engineering Economics, 5th edition, © 2010

4. Gradient-to-Equal-Payment Series Conversion Factor, (A/G, i, N)
Cash Flow Series
Factor Notation
Given: G = $1,000, N = 10 years, i = 12%
Find: A
Solution:
Contemporary Engineering Economics, 5th edition, © 2010

5. Example 3.22 – Linear Gradient: Find A, Given A1, G, i, and N
Given: A1 = $1,000, G = $300, N = 6 years, and i = 10% per year
Find: A
Contemporary Engineering Economics, 5th edition, © 2010

6. Example 3.23 Declining Linear Gradient Series
Given: A1 = $1,200, G = -$200, N = 5 years, and i = 10% per year
Find: F
Strategy: Since we have no interest formula to compute the future worth of a linear gradient series directly, we first find the equivalent present worth of the gradient series and then convert this P to its equivalent F.
Contemporary Engineering Economics, 5th edition, © 2010

7. Present Worth of Geometric Gradient Series
Formula:
Factor Notation:
Contemporary Engineering Economics, 5th edition, © 2010

8. Example 3.24 –Geometric Gradient Series
Given: A1 = $54,600, g = 7%, N = 5 years, and i = 12% per year
Find: P
Contemporary Engineering Economics, 5th edition, © 2010

9. Example 3.25 Retirement Plan – Saving $1 Million
Given: F = $1,000,000, g = 6%, i = 8%, and N = 20
Find: A1
Solution:
Contemporary Engineering Economics, 5th edition, © 2010