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 business 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 interest functions, even more widely used than the compound interest concept. You should understand this chapter on present values thoroughly, including the present value equations, before you go on to the next part of the book.

This chapter also builds on the previous chapter. Mathematical developments presented in the previous chapter, such as...