The Mathematics of Money

22 Chapter 1 Simple Interest

Now, suppose that you double the left side, turning $1,000 into $2,000. This would make

the left side “heavier” than the right, and the scale would then tilt:

$2,000

(P)(0.004)

Not =!

But, if we also doubled the right side, the scale would be back in balance:

$2,000 = (2)(P)(0.004)

And so, even if we do something that changes the “weight” on one side, we can still have

a balanced scale if we make the same change to the other side. In this example we doubled

both sides, but it should be clear that it would also have been OK to have divided both sides

in half or added $50 to both sides. Or we could have subtracted $35 from both sides had we

wanted to. And so on. The basic idea at work here is:

The Balance Principle

You can make any change you like to one side of an equation,

as long as you make an equivalent change to the other side.

Finding Principal (Revisited)

So now let’s return to the problem we were considering a moment ago. We had reached

a dead end with

$1,000  (P)(0.004)

but now the balance principle may be able to help us find P. It allows us to add anything

to, subtract anything from, multiply anything by, or divide anything into both sides that we

like. Above, we used it to double both sides, and while that is certainly allowed, it really

wasn’t much help. The resulting equation

$2,000  (2)(P)(0.004)

is true but it does nothing to get us closer to the value of P.

But now let’s ask ourselves if there might be anything that we could add, subtract,

multiply or divide that would be helpful.