Principles of Managerial Finance

semiannual compounding
Compounding of interest over
two periods within the year.

176 PART 2 Important Financial Concepts

LG5

quarterly compounding
Compounding of interest over
four periods within the year.

TABLE 4.5 The Future Value from Investing

$100 at 8% Interest Compounded

Semiannually Over 24 Months

(2 Years)

Beginning Future value Future value at end

principal interest factor of period [(1)(2)]

Period (1) (2) (3)

6 months $100.00 1.04 $104.00

12 months 104.00 1.04 108.16

18 months 108.16 1.04 112.49

24 months 112.49 1.04 116.99

4.5 Compounding Interest More

Frequently Than Annually

Interest is often compounded more frequently than once a year. Savings institu-

tions compound interest semiannually, quarterly, monthly, weekly, daily, or even

continuously. This section discusses various issues and techniques related to these

more frequent compounding intervals.

Semiannual Compounding

Semiannual compoundingof interest involves two compounding periods within

the year. Instead of the stated interest rate being paid once a year, one-half of the

stated interest rate is paid twice a year.

EXAMPLE Fred Moreno has decided to invest $100 in a savings account paying 8% interest

compounded semiannually.If he leaves his money in the account for 24 months

(2 years), he will be paid 4% interest compounded over four periods, each of

which is 6 months long. Table 4.5 uses interest factors to show that at the end of

12 months (1 year) with 8% semiannual compounding, Fred will have $108.16;

at the end of 24 months (2 years), he will have $116.99.

Quarterly Compounding

Quarterly compoundingof interest involves four compounding periods within

the year. One-fourth of the stated interest rate is paid four times a year.

EXAMPLE Fred Moreno has found an institution that will pay him 8% interestcompounded

quarterly.If he leaves his money in this account for 24 months (2 years), he will be

paid 2% interest compounded over eight periods, each of which is 3 months long.

Table 4.6 uses interest factors to show the amount Fred will have at the end of

each period. At the end of 12 months (1 year), with 8% quarterly compounding,

Fred will have $108.24; at the end of 24 months (2 years), he will have $117.16.