126 Part 2 Fundamental Concepts in Financial Management
0.05. Throughout this chapter, we designate the interest rate as I because
that symbol (or I/YR, for interest rate per year) is used on most! nancial
calculators. Note, though, that in later chapters, we use the symbol r to de-
note rates because r (for rate of return) is used more often in the! nance lit-
erature. Note too that in this chapter, we generally assume that interest
payments are guaranteed by the U.S. government; hence, they are certain.
In later chapters, we will consider risky investments, where the interest
rate earned might differ from its expected level.
INT! Dollars of interest earned during the year! Beginning amount " I. In our
example, INT! $100(0.05)! $5.
N! Number of periods involved in the analysis. In our example, N! 3. Some-
times the number of periods is designated with a lowercase n, so both N
and n indicate a number of periods.(^2) A! fth procedure, using tables that show “interest factors,” was used before! nancial calculators and computers
became available. Now, though, calculators and spreadsheets such as Excel are programmed to calculate the
speci! c factor needed for a given problem and then to use it to! nd the FV. This is more e" cient than using the
tables. Moreover, calculators and spreadsheets can handle fractional periods and fractional interest rates, such
as the FV of $100 after 3.75 years when the interest rate is 5.375%, whereas tables provide numbers only for
whole periods and rates. For these reasons, tables are not used in business today; hence, we do not discuss
them in the text.
We can use four different procedures to solve time value problems.^2 These
methods are described in the following sections.
5-2a Step-by-Step Approach
The time line used to! nd the FV of $100 compounded for 3 years at 5%, along with
some calculations, is shown.
Multiply the initial amount and each succeeding amount by (1 # I)! (1.05):
Time
Amount at beginning of period $100.00
(^0) 5% 1 2 3
$105.00 $110.25 $115.76
As noted in the text, interest earned on the interest earned
in prior periods, as was true in our example and is always
true when we apply Equation 5-1, is called compound
interest. If interest is not earned on interest, we have sim-
ple interest. The formula for FV with simple interest is
FV! PV # PV(I)(N); so in our example, FV would have been
$100 # $100(0.05)(3)! $100 # $15! $115 based on sim-
ple interest. Most financial contracts are based on com-
pound interest; but in legal proceedings, the law often
specifies that simple interest must be used. For example,
Maris Distributing, a company founded by home run king
Roger Maris, won a lawsuit against Anheuser-Busch (A-B)
because A-B had breached a contract and taken away
Maris’s franchise to sell Budweiser beer. The judge awarded
Maris $50 million plus interest at 10% from 1997 (when
A-B breached the contract) until the payment is actually
made. The interest award was based on simple interest,
which as of 2008 had raised the total from $50 million to
$50 million # 0.10($50 million)(11 years)! $105 million. If
the law had allowed compound interest, the award would
have totaled ($50 million)(1.10)^11! $142.66 million, or
$37.66 million more. This legal procedure dates back to
the days before calculators and computers. The law moves
slowly!
Compound Interest
Occurs when interest is
earned on prior periods’
interest.
Simple Interest
Occurs when interest is not
earned on interest.
Compound Interest
Occurs when interest is
earned on prior periods’
interest.
Simple Interest
Occurs when interest is not
earned on interest.
SIMPLE VERSUS COMPOUND INTEREST