Note that the account yields 5% interest per year, compounded annually?
•
From above problem:
•
P = $10,000
•
i = 5%
•
n = 5 years
•
Consider uniform series capital recover factor:
A = P * (A/P,i%,n) = $10,000 * (A/P,5%,5) = $10,000 * 0.23097 = $2,309.70
•
Note: 0.23096 is obtained from appendix A
–
compound interest factor for interest rate =
5.00%.
•
Therefore,
you need to withdraw $2,309.70 for 5 years so that the account can be depleted
at the end of 5 years.
13
IE 492
–
Engineering Economics

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UNIFORM SERIES PRESENT WORTH
FACTOR
•
Uniform series present worth factor calculates the amount that must be invested today in order to be
able to withdraw a fixed amount every year for n years, when the invested amount earns interest i
per year, compounded annually.
•
Uniform series present worth factor is reciprocal of the uniform series capital recovery factor.
•
Uniform series capital recovery factor formula:
A = P * i(1+i)
n
/ [(1 + i)
n
–
1]
Therefore, A/P = i(1+i)
n
/ [(1 + i)
n
–
1] = i/[1-(1+i)
-n
]
Therefore, P/A = (A/P)
-1
= [(1 + i)
n
–
1] / i(1+i)
n
•
Therefore, the ratio, P/A is called the uniform series present worth factor.
•
Numerical values of this factor are shown in Appendix A of the book.
•
A fuller notation for this factor is: (P/A,i%,n)
Let’s look at an example on the next slide.
14
IE 492
–
Engineering Economics

UNIFORM SERIES PRESENT WORTH
FACTOR (EXAMPLE)
•
You decide to withdraw $2,309.70 at the end of each year from your investment account for 5
years. After 5 years you expect to have depleted the account balance and wish to close the
account. How much money should you deposit in the account today, if the account yields 5%
interest per year, compounded annually?
•
From above problem:
•
A = $2,309.70
•
i = 5%
•
n = 5 years
•
Consider uniform series capital recover factor:
P = A * (P/A,i%,n) = A * (A/P,i%,n)
-1
= $2,309.70 * (A/P,5%,5)
-1
= $2,309.70 * (0.23097)
-1
=
$10,000
•
Note: 0.23097 is obtained from appendix A
–
compound interest factor for interest rate =
5.00%.
•
Therefore,
you need to withdraw invest $10,000 today so you can withdraw $2,309.70 for 5
and account can be depleted after the fifth withdrawal.
15
Note: Uniform series
present worth factor is
reciprocal of Uniform
series capital recovery
factor
IE 492
–
Engineering Economics

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GRADIENT SERIES FACTOR
•
Gradient series is a series of payments that either increases or decreases each by a constant
amount.
•
Payments are made at the end of at the beginning of each period.
•
The delta i.e. increase or decrease amount is called as gradient.
•
If the increase or decrease amount is a constant amount then the series is called as Arithmetic
Gradient Uniform Series. E.g. amount is $500, $1000, -$500, -$2000 etc.

- Summer '16