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

20.4 Effective Interest Rate

If you deposit $100.00 in a savings account, at 6% compounding monthly, then, using

Equation (20.3), at the end of one year you will have $106.16 in your account. The $6.16

earned during the first year is higher than the stated 6% interest, which could be understood

as $6.00 for a $100.00 deposit over a period of one year. In order to avoid confusion, the stated

or the quoted interest rate is called the nominal interest rate, and the actual earned interest rate

is called the effective interest rate. The relationship between the nominal rate,i, and the effec-

tive rate,ieff, is given by

(20.4)

wheremrepresents the number of compounding periods per year. To better understand the

compounding effect of interest, let us see what happens if we deposit $100.00 in an account

for a year based on one of the following quoted interests: 6% compounding annually, 6% semi-

annually, 6% quarterly, 6% monthly, and 6% daily. Table 20.4 shows the difference among

these compounding periods, the total amount of money at the end of one year, the interest

earned, and the effective interest rates for each case.

When comparing the five different interest compounding frequencies, the difference in the

interests earned on a $100.00 investment, over a period of a year, may not seem much to you,

but as the principal and the time of deposit are increased this value becomes significant. To better

demonstrate the effect of principal and time of deposit, consider the following example.

ieffa 1 

i

m

b

m

 1

20.4 Effective Interest Rate 661

TABLE 20.4 The Effect of the Frequency of Interest Compounding Periods

Total

Number of Total Amount Interest Effective

Compounding Compounding after 1 Year (dollars Interest

Period Periods (dollars and cents) and cents) Rate

Annually 1 100(1 0.06) 106.00 6.00 6%

Semiannually 2 6.09 6.09%

Quarterly 4 6.13 6.13%

Monthly 12 6.16 6.16%

Daily 365 100 a 1  6.18 6.18%

0.06

365

b

365

106.18

100 a 1 

0.06

12

b

12

106.16

100 a 1 

0.06

4

b

4

106.13

100 a 1 

0.06

2

b

2

106.09

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