Lecture No.7
Chapter 3
Contemporary Engineering Economics
Copyright © 2010
Contemporary Engineering Economics, 5th edition, © 2010
Equal Payment Series
0
A
A
1
F
2
N
A
P
0
1
2
N
0
Contemporary Engineering Economics, 5th edition, © 2010
N
Equal-Payment Series Compound Amount Factor
 Formula
F
A
A
A
0 1
2
N
0
1
2
N
F
=
0 1
2
N
A
A
A
Contemporary Engineering Economics, 5th edition, © 2010
An Alternate Way of Calculating the
Equivalent Future Worth, F
F
A
A(1+i)N-2
A
A
A
A(1+i)N-1
0
1
2
N
F  A(1  i)N 1  A(1  i)N 2 
0
1
2
 (1  i)N  1 
 A  A

i


Contemporary Engineering Economics, 5th edition, © 2010
N
Example 3.14 Uniform Series: Find F, Given i, A, and N
 Given: A = $3,000, N = 10
years, and i = 7% per year
 Find: F
 Excel Solution:
Contemporary Engineering Economics, 5th edition, © 2010
Example 3.15 Handling Time Shifts: Find F, Given i, A, and N
 Given: A = $3,000, N = 10
years, and i = 7% per year
 Find: F
o Each payment has been shifted to one year
 Excel Solution:
earlier, thus each payment would be compounded
for one extra year
Contemporary Engineering Economics, 5th edition, © 2010
Sinking-Fund Factor: Find A, Given i, N, and F
 Given: F = $5,000, N = 5
years, and i = 7% per year
 Formula – Sinking Fund Factor
 Find: A
A  $5,000(A / F ,7%,5)
 $869.50
A  $5,000(A / F ,7%,5)
 $869.50
$5,000
 Excel Solution:
0
1
5
=PMT(7%,5,0,5000)
A
Contemporary Engineering Economics, 5th edition, © 2010
Example 3.17 Comparison of Three Different Investment Plans
 Given: Three investment
plans and i = 8%
 Find: Balance on the 65th
birthday
Contemporary Engineering Economics, 5th edition, © 2010
How Long
Would It
Take to Save
$1 Million?
Contemporary Engineering Economics, 5th edition, © 2010
Example 3.18 Uniform Series: Find A, Given P, i, and N
 Given: P = $250,000, N = 6
years, and i = 8% per year
 Capital Recovery Factor
 Find: A
 Formula to use:
 Excel Solution:
Contemporary Engineering Economics, 5th edition, © 2010
Example 3.19 – Deferred Loan Repayment
 Given: P = $250,000, N = 6
years, and i = 8% per year, but
the first payment occurs at the
end of year 2
 Find: A
Step 1: Find the equivalent
amount of borrowing at the end
of year 1:
 Step 2: Use the capital
recovery factor to find the size
of annual installment:
Contemporary Engineering Economics, 5th edition, © 2010
Example 3.20 Uniform Series: Find P, Given A, i, and N
 Given: A = $10,576,923, N =
26 years, and i = 5% per year
 Present Worth Factor
 Find: P
 Formula to use:
 Excel Solution:
Contemporary Engineering Economics, 5th edition, © 2010