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

658 Chapter 20 Engineering Economics

TABLE 20.1 The Effect of Compounding Interest

Balance at the Interest for Balance at the End

Beginning of the Year at of the Year, Including

the Year (dollars 6% (dollars the Interest (dollars

Year and cents) and cents) and cents)

1 100.00 6.00 106.00

2 106.00 6.36 112.36

3 112.36 6.74 119.10

4 119.10 7.14 126.24

5 126.24 7.57 133.81

6 133.81 8.02 141.83

Simple interests are very rare these days! Almost all interest charged to borrow accounts or

interest earned on money deposited in a bank is computed using compound interest. The con-

cept of compound interest is discussed next.

Compound Interest

Under the compounding interest scheme, the interest paid on the initial principal will also

collect interest. To better understand how the compound interest earned or paid on a principal

works, consider the following example. Imagine that you put $100.00 in a bank that pays you

6% interest compounding annually. At the end of the first year (or the beginning of the second

year) you will have $106.00 in your bank account. You have earned interest in the amount of

$6.00 during the first year. However, the interest earned during the second year is determined

by ($106.00)(0.06) $6.36. That is because the $6.00 interest of the first year also collects 6%

interest, which is 36 cents itself. Thus, the total interest earned during the second year is $6.36,

and the total amount available in your account at the end of the second year is $112.36. Com-

puting the interest and the total amount for the third, fourth, fifth and the sixth year

in a similar fashion will lead to $141.83 in your account at the end of the sixth year. Refer to

Table 20.1 for detailed calculations. Note the difference between $100.00 invested at 6% sim-

ple interest and 6% interest compounding annually for a duration of six years. For the simple

interest case, the total interest earned, after six years, is $36.00, whereas the total interest accu-

mulated under the annual compounding case is $41.83 for the same duration.

20.3 Future Worth of a Present Amount

Now we will develop a general formula that you can use to compute the future valueFof any pres-

ent amount (principal)P, afternyears collectingi% interest compounding annually. The cash flow

diagram for this situation is shown in Figure 20.3. In order to demonstrate, step-by-step, the com-

pounding effect of the interest each year, Table 20.2 has been developed. As shown in Table 20.2,

starting with the principalP, at the end of the first year we will havePPiorP(1i). During the

second year, theP(1i) collects interest in an amount ofP(1i)i, and by adding the interest to

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