Principles of Managerial Finance

CHAPTER 4 Time Value of Money 179

116.99

100 PV

N

CPT

FV

I

4

4

Solution

Input Function

117.17

100 PV

N

CPT

FV

I

8

2

Solution

Input Function

continuous compounding
Compounding of interest an
infinite number of times per year
at intervals of microseconds.

10. Most calculators have the exponential function, typically noted by ex,built into them. The use of this key is espe-
    cially helpful in calculating future value when interest is compounded continuously.

Comparing the calculator, table, and spreadsheet values, we can see that the

calculator and spreadsheet values agree generally with the values in Table 4.7 but

are more precise because the table factors have been rounded.

Continuous Compounding

In the extreme case, interest can be compounded continuously. Continuous

compoundinginvolves compounding over every microsecond—the smallest time

period imaginable. In this case, min Equation 4.20 would approach infinity.

Through the use of calculus, we know that as mapproaches infinity, the equation

becomes

FVn(continuous compounding)PV(ein) (4.21)

where eis the exponential function^10 , which has a value of 2.7183. The future

value interest factor for continuous compounding is therefore

FVIFi,n(continuous compounding)ein (4.22)

Table Use Multiplying each of the future value interest factors by the initial

$100 deposit results in a value of $117.00 (1.170$100) for semiannual com-

pounding and a value of $117.20 (1.172$100) for quarterly compounding.

Calculator Use If the calculator were used for the semiannual compounding

calculation, the number of periods would be 4 and the interest rate would be

4%. The future value of $116.99 will appear on the calculator display as

shown at the top left.

For the quarterly compounding case, the number of periods would be 8 and

the interest rate would be 2%. The future value of $117.17 will appear on the calcu-

lator display as shown in the second display at the left.

Spreadsheet Use The future value of the single amount with semiannual and

quarterly compounding also can be calculated as shown on the following Excel

spreadsheet.