1. Interest Formulas (Gradient Series)
Lecture No. 8
Chapter 3
Contemporary Engineering Economics
Copyright © 2016

2. Linear Gradient Series
AStrictGradientSeries
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

3. Example 3.18:LinearGradient: Find P, Given A1, G, N, and i
Given: A1 = $1,000, G= $250,N = 5 years, and i = 12% per year
Find: P

4. Solution
Excel Solution

5. 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

6. Example 3.19: 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

7. Solution

8. Example 3.20: Declining Linear Gradient Series: Find F, Given A1, G, I, and N
G = -$200, N = 5 years, and i = 10% per year
Find: F

9. Solution
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.
Solution

10. Present Worth of Geometric Gradient Series
Formula
Factor Notation

11. Example 3.21: Geometric Gradient Series
Given: A1 = $54,600, g = 7%, N = 5 years, and i = 12% per year
Find: P

12. Solution

13. Example 3.22: Retirement Plan: Saving $1 Million
Given:
F = $1,000,000,
g = 6%,
i = 8%, and
N = 20
Find: A1

14. Solution