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

664 Chapter 20 Engineering Economics

To obtain the relationship betweenPandA, we will treat each future payment separately

and relate each payment to its present equivalent value using Equation (20.5); we then add all

the resulting terms together. This approach leads to the following relationship:

(20.6)

As you can see, Equation (20.6) is not very user-friendly, so we need to simplify it somehow.

What if we were to multiply both sides of Equation (20.6) by the term (1 i)? This operation

results in the following relationship:

(20.7)

Now if we subtract Equation (20.6) from Equation (20.7), we have

(20.8)

Simplifying the right-hand side of Equation (20.8) leads to the following relationship:

(20.8b)

And after simplifying the left-hand side of Equation (20.8), we have

(20.8c)

Now if we divide both sides of Equation (20.8c) byi, we have

(20.9)

Equation (20.9) establishes the relationship between the present value of a lump sumPand its

equivalent uniform series paymentsA. We can also rearrange Equation (20.9), to representA

in terms ofPdirectly, as given by the following formula:

(20.10)

20.7 Future Worth of Series Payment

To develop a formula for computing the future worth of a series of uniform payments, we

begin with the relationship between the present worth and the future worth, Equation (20.2),

and then we substitute forPin Equation (20.2) in terms ofA, using Equation (20.9). This

A

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