Principles of Managerial Finance

CHAPTER 4 Time Value of Money 155

compound interest
Interest that is earned on a given
deposit and has become part of
the principal at the end of a
specified period.

principal
The amount of money on which
interest is paid.

future value
The value of a present amount at
a future date, found by applying
compound interestover a
specified period of time.

LG2

Review Questions

4–1 What is the difference betweenfuture valueandpresent value?Which

approach is generally preferred by financial managers? Why?

4–2 Define and differentiate among the three basic patterns of cash flow: (1) a

single amount, (2) an annuity, and (3) a mixed stream.

4.2 Single Amounts

The most basic future value and present value concepts and computations con-

cern single amounts, either present or future amounts. We begin by considering

the future value of present amounts. Then we will use the underlying concepts to

learn how to determine the present value of future amounts. You will see that

although future value is more intuitively appealing, present value is more useful

in financial decision making.

Future Value of a Single Amount

Imagine that at age 25 you began making annual purchases of $2,000 of an invest-

ment that earns a guaranteed 5 percent annually. At the end of 40 years, at age 65,

you would have invested a total of $80,000 (40 years$2,000 per year). Assum-

ing that all funds remain invested, how much would you have accumulated at the

end of the fortieth year? $100,000? $150,000? $200,000? No, your $80,000

would have grown to $242,000! Why? Because the time value of money allowed

your investments to generate returns that built on each other over the 40 years.

The Concept of Future Value

We speak of compound interestto indicate that the amount of interest earned on

a given deposit has become part of the principal at the end of a specified period.

The term principalrefers to the amount of money on which the interest is paid.

Annual compounding is the most common type.

The future valueof a present amount is found by applying compound interest

over a specified period of time. Savings institutions advertise compound interest

returns at a rate of xpercent, or x percent interest, compounded annually, semi-

annually, quarterly, monthly, weekly, daily, or even continuously. The concept of

future value with annual compounding can be illustrated by a simple example.

EXAMPLE If Fred Moreno places $100 in a savings account paying 8% interest com-

pounded annually, at the end of 1 year he will have $108 in the account—the ini-

tial principal of $100 plus 8% ($8) in interest. The future value at the end of the

first year is calculated by using Equation 4.1:

Future value at end of year 1$100(10.08)$108 (4.1)

If Fred were to leave this money in the account for another year, he would be

paid interest at the rate of 8% on the new principal of $108. At the end of this