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

procedure is demonstrated, step-by-step, next. The relation between a present value and a

future value is given by Equation (20.2):

(20.2)

And the relationship between the present worth and a uniform series is given by Equation (20.9):

(20.9)

Substituting into Equation (20.2) forPin terms ofAusing Equation (20.9), we have

(20.11)

Simplifying Equation (20.11) results in the direct relationship between the future worthFand

the uniform payments or depositsA, which follows:

(20.12)

And by rearranging Equation (20.12), we can obtain a formula forAin terms of future

worthF:

(20.13)

Now that we have all the necessary tools, we turn our attention to the question we asked

earlier about how much money you need to put aside every year for the next five years to have

$2000 for the down payment of your car when you graduate. Recall that the interest rate is

6.5% compounding annually. The annual deposits are calculated from Equation (20.13), which

leads to the following amount:

Putting aside $351.26 in a bank every year for the next five years may be more manageable

than depositing a lump sum of $1459.76 today, especially if you don’t currently have access to

that large a sum!

It is important to note that Equations (20.9), (20.10), (20.12), and (20.13) apply to a

situation wherein the uniform series of payments or revenuesoccur annually. Well, the next

question is, how do we handle situations where the payments are made monthly? For example,

a car or a house loan payment occurs monthly. Let us now modify our findings by considering

the relationship between present valuePand uniform series payments or revenueAthat occur

more than once a year at the same frequency as the frequency of compounding interest per

A 2000 c

0.065

11 0.065 2

5

 1

d$351.26

AF c

i

11 i 2

n

 1

d

FAc

11 i 2

n

 1

i

d

FP 11 i 2

n

Ac

11 i 2

n

 1

i 11 i 2

n d1^1 i^2

n

u

P

PAc

11 i 2

n

 1

i 11 i 2

n d

FP 11 i 2

n

20.7 Future Worth of Series Payment 665

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