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

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

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

Solution Excel Solution

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

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

Solution

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

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

Present Worth of Geometric Gradient Series Formula Factor Notation

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

Solution

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

Solution