Principles of Managerial Finance

CHAPTER 4 Time Value of Money 177

TABLE 4.6 The Future Value from Investing

$100 at 8% Interest Compounded

Quarterly Over 24 Months

(2 Years)

Beginning Future value Future value at end

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

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 1.02 110.40

18 months 110.40 1.02 112.61

21 months 112.61 1.02 114.86

24 months 114.86 1.02 117.16

TABLE 4.7 The Future Value at the End of

Years 1 and 2 from Investing $100

at 8% Interest, Given Various

Compounding Periods

Compounding period

End of year Annual Semiannual Quarterly

1 $108.00 $108.16 $108.24

2 116.64 116.99 117.16

Table 4.7 compares values for Fred Moreno’s $100 at the end of years 1 and
2 given annual, semiannual, and quarterly compounding periods at the 8 percent
rate. As shown,the more frequently interest is compounded, the greater the
amount of money accumulated.This is true forany interest rateforany period
of time.

A General Equation for Compounding

More Frequently Than Annually

The formula for annual compounding (Equation 4.4) can be rewritten for use
when compounding takes place more frequently. If mequals the number of times
per year interest is compounded, the formula for annual compounding can be
rewritten as

FVnPV 1  

mn

(4.20)

i



m