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55
CHAPTER 4: FUTURE VALUE, PRESENT VALUE AND
INTEREST RATES
A. T
HE
B
ASICS
The primary focus in this chapter is on Core Principle 1: time has value. It is
likely that your success in this part of the course, and in many aspects of your financial
life far beyond this course, depend crucially on understanding this chapter. If you learn
the concepts, and how to implement them, you will earn huge rewards.
Chapter 4 is organized around three topics. First, the ideas of future and present
values are presented. You will start with the notion of future values, and in the process
highlight the notion of compound interest. You will also see that the idea of the present
value is one that is closely related to future value. In fact, much as division “undoes”
multiplication (take a number, double it, and then divide by two), present value and
future value are really concepts where one “undoes” the other. Second, in the process of
discovering the ideas of present and future value, you will at the same time be learning
about the proper measure of the interest rate as a way to correctly measure the time value
of money. Third, it is absolutely imperative for you to learn to distinguish between what
economists call the nominal interest rate and the real interest rate. This distinction arises
whenever the rate of price change is not zero. In many important ways the real interest
rate is the focus of monetary policy, as you will begin learning at the end of the chapter.
B. S
OLIDIFY
Y
OUR
K
NOWLEDGE
DISCUSSION/EXTENSIONS OF THE BASICS
The Key Equation
: Text equation (3) on page 74 is the most important expression
in the chapter. It states:
PV = FV
n
/ (1+i)
n
.
Note that an algebraic equivalent, FV
n
= PV * (1+i)
n
on text page 72, is similarly
important. These expressions show explicitly and precisely the value of time. The
expression in terms of FV
n
helps understand the concept of compounding. The expression
in terms of PV helps you grasp how financial assets, which often provide promises to
make payments in the future, are priced today.
The Real Interest Rate
. The real interest rate is a key concept. For a sense of its
importance, take a quick look ahead at
Your Financial World
: It’s the Real Interest Rate
that Matters on text page 558 in chapter 21.
The “nominal” interest rate tells how much you will receive later in dollars if you
make a loan today. For example, lend someone $1 at 5%, and in a year you will have

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$1.05. Similarly, the nominal rate tells you the dollar amount you will owe later if you
take out a loan today. Borrow $1 at 5% and next year you will owe $1.05. In contrast, the
real interest rate tells how much you will earn (or pay) in terms of goods (and services)
rather than in terms of dollars. Lend someone a “bundle” of goods today and receive back

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