2 - Mathematical Preliminaries – Working with Interest Rates

Summary

Learning Objectives

In this chapter, we will review the concepts of interest rates and time value of money (TVM). There are several types of present-value and future-value formulas, each of which is used in specific circumstances. Our goal is to make sure that you understand when (i.e., in what context) these formulas should be used. A good understanding of this chapter is needed to proceed to future chapters, where we will need to calculate the amounts of your consumption and savings at various points in time.

Although we believe that most of you have covered these materials in your previous finance courses, we recommend that you take another look at them and familiarize yourself with the notations we will use in the rest of this book.

Interest Rates

As you may recall, an interest rate is the rate of return that a borrower promises to pay for the use of money that he or she borrows from the lender. Normally, it is expressed in terms of per-annum percentage rates (e.g., 4% p.a.). To express it properly, however, we also need to state the compounding frequency of the rate, which is the number of compounding periods in one year. In other words, it is the number of times in a year that interest is calculated and added to the principal of the loan.

For example, annual compounding means that interest is added to the principal once a year. Suppose you invest $1 for one year at the interest rate of 4% p.a., annual compounding.