Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

668 Chapter 20 Engineering Economics

TABLE 20.7 A Summary of Formulas for Situations wheniCompounds Annually

and the Uniform SeriesAOccurs Annually

To Find Given Use This Formula Interest –Time Factor

FP FP(1 i)

n

(F/P,i,n) (1 i)

n

PF

PA

AP

FA

AF 1 A /F, i, n 2 c

1 i 2

11 i 2 n 1

AF c d

1 i 2

11 i 2 n 1

d

1 F /A, i, n 2 c

11 i 2

n

 1

i

FAc d

11 i 2

n

 1

i

d

1 A /P, i, n 2 c

1 i 211 i 2 n

11 i 2

n

 1

AP c d

1 i 211 i 2 n

11 i 2

n

 1

d

1 P /A, i, n 2 c

11 i 2 n 1

i 11 i 2

PAc n d

11 i 2 n 1

i 11 i 2

n d

1 P /F, i, n 2 

1

11 i 2 n

P

F

11 i 2 n

Alternatively, first, we could have computed the ieffthat matches the deposits frequency and

then used it to compute the future value. These steps are

20.8 Summary of Engineering Economics Analysis

The engineering economics formulas that we have developed so far are summarized in

Tables 20.7 and 20.8. The definitions of the terms in the formulas are given here:

P present worth, or present cost — lump sum ($)

F future worth, or future cost — lump sum ($)

A uniform series payment, or uniform series revenue ($)

i nominal interest rate

ieffeffective interest rate

n number of years

mnumber of interest compounding periods per year

The interest – time factors shown in the fourth column of Table 20.7 are used as shortcuts to

avoid writing long formulas when evaluating equivalent values of various cash flow occurrences.

F 20001 F/A. 4.56%, 4 2  2000 c

11 0.0456 2

4

 1

0.0456

d$8,564.02

ieff a 1 

0.045

3

b

3

 1 0.0456

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