Interest Formulas – Gradient Series
Download
Report
Transcript Interest Formulas – Gradient Series
Lecture No.8
Chapter 3
Contemporary Engineering Economics
Copyright © 2010
Contemporary Engineering Economics, 5th edition, © 2010
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
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
Gradient-to-Equal-Payment Series Conversion Factor,
(A/G, i, N)
Cash Flow Series
Given: G = $1,000, N = 10
years, i = 12%
Find: A
Solution:
A $1,000(A / G ,12%,10)
$1,000(3.5847)
Factor Notation
$3,584.70
Contemporary Engineering Economics, 5th edition, © 2010
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
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
Present Worth of Geometric Gradient Series
Formula:
Factor Notation:
Contemporary Engineering Economics, 5th edition, © 2010
Example 3.24 –Geometric Gradient Series
Given: A1 = $54,600, g = 7%,
N = 5 years, and i = 12% per
year
Find: P
1 (1 0.07)5 (1 0.12)5
POld $54,600
0.12
0.07
$222,937
PNew $54,600(1 0.23)(P / A,12%,5)
$42,042(3.6048)
$151,552
Contemporary Engineering Economics, 5th edition, © 2010
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