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

666 Chapter 20 Engineering Economics

year. For this situation, Equation (20.9) is modified to incorporate the frequency of com-

pounding interest per year,m, in the following manner:

(20.14)

Note that in order to obtain Equation (20.14), we simply substituted in Equation (20.9) fori,

i/m, and forn,nm. Equation (20.14) can be rearranged to solve forAin terms ofPaccording to

(20.15)

Similarly, Equations (20.12) and (20.13) can be modified for situations whereAoccurs more

than once a year — at the same frequency as the compounding interest — leading to the

following relationship:

(20.16)

(20.17)

Finally, when the frequency of uniform series is different from the frequency of com-

pounding interest,ieffmust first be calculated to match the frequency of the uniform series.

Example 20.7 Let us return to the question we asked earlier about how much money you need to put aside

for the next five years to have $2000 for the down payment on your car when you graduate.

Now consider the situation where you make your deposits every month, and the interest rate

is 6.5% compounding monthly.

The deposits are calculated from Equation (20.17), which leads to the following:

Putting aside $28.29 in the bank every month for the next five years is even more manageable

than depositing $351.26 in a bank every year for the next five years, and it is certainly more

manageable than depositing a lump sum of $1459.76 in the bank today!

AF ≥

i

m

a 1 

i

m

b

mn

 1

¥ 2000 ≥

0.065

12

a 1 

0.065

12

b

1122 152

 1

¥$28.29

AF ≥

i

m

a 1 

i

m

b

1 m 2 1 n 2

 1

¥

FA≥

a 1 

i

m

b

1 m 2 1 n 2

 1

i

m

¥

AP ≥

a

i

m

ba 1 

i

m

b

nm

a 1 

i

m

b

nm

 1

¥

PA≥

a 1 

i

m

b

nm

 1

i

m

a 1 

i

m

b

nm ¥

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