 CHAPTER
4
Present Values
Chapter 3 showed how someone who started with a certain amount of money
would answer the question, “How much will I have in a given time at a given
interest rate?” This chapter covers the opposite case. Suppose you need a
certain amount of money at a deﬁnite future time, and you have an interest
rate you can earn. How much must you set aside now to make sure you have
the required future amount at the required future time? This is called a present
value. In this chapter, we look at the present value equations and at present
value interest tables and we examine how the present values change as
interest rate and time change.
We then use the present value concept to analyze a proposed project, so we
can determine whether or not we should proceed with the project. We use this
present value analysis of a project to develop the concept of internal rate of
return. This is a common problem in many activities, including many busi-
ness applications.
We will use the concept of present value throughout this book. It is the
most important of the concepts we present in the chapters on compound inter-
51

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