4 Chapter 1 Simple Interest
Definition 1.1.4
A debtor is someone who owes someone else money. A creditor is someone to whom money
is owed.In Example 1.1.1 Sam is Danielle’s creditor and Danielle is Sam’s debtor. In Example 1.1.2
we would say that Tom is Larry’s creditor and Larry is Tom’s debtor.Definition 1.1.5
The amount of time for which a loan is made is called its term.In Example 1.1.1 the term is 100 days. In Example 1.1.2 the term of the loan is 1 year.Interest Rates as Percents
Let’s reconsider Tom and Larry’s loan from Example 1.1.2 for a moment. Tom and Larry
have agreed that the interest Tom will charge for a loan is $50. Now suppose Larry decides
that, instead of borrowing $200, he needs to borrow $1,000. He certainly can’t expect that
Tom will still charge the same $50 interest! Common sense screams that for a larger loan
Tom would demand larger interest. In fact, it seems reasonable that for 5 times the loan, he
would charge 5 times as much interest, or $250.
By the same token, if this loan were for $200,000 (one thousand times the original
principal) we could reasonably expect that the interest would be $50,000 (one thousand
times the original interest.) The idea here is that, as the size of the principal is changed, the
amount of interest should also change in the same proportion.
For this reason, interest is often expressed as a percent. The interest Tom was charging
Larry was^1 ⁄ 4 of the amount he borrowed, or 25%. If Tom expresses his interest charge as a
percent, then we can determine how much he will charge Larry for any size loan.Example 1.1.3 Suppose that Larry wanted to borrow $1,000 from Tom for 1 year.
How much interest would Tom charge him?Tom is charging 25% interest, and 25% (or ¼) of $1,000 is $250. So Tom would charge
$250 interest. Note that $250 is also 5 times $50, and so this answer agrees with our
commonsense assessment!Of course, the situation here is simplified by the fact that 25% of $1,000 is not all that hard
to figure out. With less friendly numbers, the calculation becomes a bit trickier. What if,
for example, we were trying to determine the amount of interest for a loan of $1835.49
for 1 year at 11.35% simple interest? The idea should be the same, though the calculation
requires a bit more effort.Working with Percents
When we talk about percents, we usually are taking a percent of something. The math-
ematical operation that translates the “of” in that expression is multiplication. So, to find
25% of $1,000, we would multiply 25% times $1,000.
However, if I simply multiply 25 times 1,000 on my calculator, I get 25,000, which is
far too big and also does not agree with the answer of $250 which we know is correct. The
reason for this discrepancy is that 25% is not the same as the number 25. The word percent
comes from Latin, and means “out of 100.” So when we say “25%,” what we really mean
is “25 out of 100”—or in other words 25/100.
If you divide 25/100 on a calculator, the result is 0.25. This process of converting a percent
into its real mathematical meaning is often called converting the percent to a decimal.
It is not necessary, though, to bother with dividing by 100 every time we need to use
a percent. Notice that when we divided 25 by 100, the result still had the same 25 in it,
just with a differently placed decimal. Now we don’t normally bother writing in a decimal
place with whole numbers, but we certainly can. 25 can be written as “25.”; now 0.25 is