Introduction to Corporate Finance

PART 1: INTRODUCTION

Semiannual Compounding

The semiannual compounding of interest involves two compounding periods within the year. Instead of the

stated interest rate being paid once per year, one-half of the rate is paid twice a year.

To demonstrate, consider an opportunity to deposit $100 in a savings account paying 8% interest with

semiannual compounding. After the first six months, your account grows by 4% to $104. Six months later,

the account again grows by 4% to $108.16. Notice that after one year, the total increase in the account

value is $8.16, or 8.16% ($8.16 ÷ $100.00). This return slightly exceeds the stated rate of 8% because

semiannual compounding allows you to earn interest on interest during the year, increasing the overall rate

of return. Table 3.1 shows how the account value grows every six months for the first two years. At the

end of two years, the account value reaches $116.99.

TABLE 3.1 THE FUTURE VALUE FROM INVESTING $100 AT 8% INTEREST COMPOUNDED SEMIANNUALLY

OVER TWO YEARS

Period Beginning principal (1) Future value factor (2)

Future value at end of

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

Quarterly Compounding

As the name implies, quarterly compounding describes a situation in which interest compounds four times

per year. An investment with quarterly compounding pays one-fourth of the stated interest rate every

three months.

For example, assume that after further investigation, you find an institution that pays 8% interest

compounded quarterly. After three months, your $100 deposit grows by 2% to $102. Three months

later, the balance again increases 2% to $104.04. By the end of the year, the balance reaches $108.24.

Table 3.2 tracks the growth in the account every three months for two years. At the end of two years,

the account is worth $117.17, which is greater than the sum attained after two years with semiannual

compounding.

TABLE 3.2 THE FUTURE VALUE FROM INVESTING $100 AT 8% INTEREST COMPOUNDED QUARTERLY OVER

TWO YEARS

Period Beginning principal (1) Future value factor (2)

Future value at end of

period [(1) × (2)] (3)

3 months $100.00 1.02 $102.00

6 months 102.00 1.02 104.04

9 months 104.04 1.02 106.12

12 months 106.12 1.02 108.24

15 months 108.24 1.02 110.41

18 months 110.41 1.02 112.62

21 months 112.62 1.02 114.87

24 months 114.87 1.02 117.17

semiannual compounding
Interest compounds twice
a year.

quarterly compounding
Interest compounds four times
per year