Copyright © 2008, The McGraw-Hill Companies, Inc.
1.3 Determining Principal, Interest Rates, and Time
So far, we have developed the ability to calculate the amount of interest due when we know
the principal, rate and time. However, situations may arise where we already know the
amount of interest, and instead need to calculate one of the other quantities. For example,
consider these situations:A retiree hopes to be able to generate $1,000 income per month from an investment
account that earns 4.8% simple interest. How much money would he need in the
account to achieve this goal?
Jim borrowed $500 from his brother-in-law, and agreed to pay back $525 ninety days
later. What rate of simple interest is Jim paying for this loan, assuming that they agreed
to calculate the interest with bankers’ rule?
Maria deposited $9,750 in a savings account that pays 5^1 ⁄^4 % simple interest. How long
will it take for her account to grow to $10,000?In this section, we will figure out how to deal with questions of these types.Finding Principal
Let’s begin by considering the situation of the retiree from above. Since this is a situation
of simple interest, it seems reasonable to approach the problem by using the simple interest
formula we developed in Section 1.2.
We know the amount of interest is $1,000, and so I $1,000. We know the interest rate
is 4.8%, so R 0.048. Also, since the interest needs to be earned in a month, we know that
T 1/12. Plugging these values into the formula, we get:I = PRT
$1,000 = (P)(0.048)(1/12)We can at least multiply the (0.048)(1/12) to get:$1,000 = (P)(0.004)But now it seems we’re stuck. In our earlier work, to find I all we needed to do was mul-
tiply the numbers and the formula handed it to us directly. Here, though, P is caught in the
middle of the equation. We clearly need some other tools to get it out. We will be able to do
this by use of the balance principle.The Balance Principle
When we write an equation, we are making the claim that the things on the left side of the
“=” sign have the exact same value as the things on the other side. We can visualize this
by thinking of an equation as a balanced scale. The things on the left side of the equal sign
are equal to the things on the right. If we imagine that we placed the contents of each side
on a scale, it would balance.
Using this idea with our present situation, $1,000 (P)(0.004), we’d have:$1,000 = (P)(0.004)
1.3 Determining Principal, Interest Rates, and Time 21