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

Example 20.8 Determine the monthly payments for a five-year, $10,000 loan at an interest rate of 8% com-

pounding monthly.

To calculate the monthly payments, we use Equation (20.15).

Example 20.9 In this example problem, we show how to deal with situations when the frequency of uniform

series is different from the frequency of compounding interest. As we mentioned previously, you

must first calculate an ieffthat matches the frequency of uniform series. Consider the following

situations in which you deposit $2000 every three months for one year. (a) The interest is 18%

compounding quarterly. (b) The interest is 18% compounding monthly. Compare the future

values of the deposits at the end of year one.

When following the solution, note that deposits are made at the end of the current month

or the beginning of the next month. In part (a), the frequency of deposits matches the interest

compounding frequency. Consequently, the future value is simply calculated from

In part (b), the interest compounding frequency is 12, whereas the frequency of deposits

is 4. In order to understand how part (b) differs from part (a), let us look at the balance at the

beginning and the end of each month, as shown in Table 20.6.

As you can see for situation (b), at the end of year 1, the future value of the deposits is

$8,564.99, which is slightly higher than the value for situation (a) at $8,556.38.

F 2000 1 F/A, 4.50%, 4 2  2000 c

11 0.045 2

4

 1

0.045

d$8,556.38

AP ≥

a

i

m

ba 1 

i

m

b

nm

a 1 

i

m

b

nm

 1

¥10,000≥

a

0.08

12

ba 1 

0.08

12

b

60

a 1 

0.08

12

b

60

 1

¥$202.76

20.7 Future Worth of Series Payment 667

TABLE 20.6 Balance at the Beginning and the End of Each Month for Example 20.9

Balance at the Balance at the End of

Beginning of Months Interest for the Month the Month(dollars

Month (dollars and cents) at 1.5% (dollars and cents) and cents)

1 0.00 0.00 0.00

2 0.00 0.00 0.00

3 0.00 0.00 0.00

4 2000 30.00 2030.00

5 2030.00 30.45 2060.45

6 2060.45 30.90 2091.35

7 2000 2091.354091.35 61.37 4152.72

8 4152.72 62.29 4215.01

9 4215.01 63.22 4278.23

10 2000 4278.236278.23 94.17 6372.40

11 6372.40 95.58 6467.98

12 6467.98 97.01 6564.99

2000 6564.998,564.99

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