The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

(^4) Actually this is not quite true. Zero divided by zero is not one, it is undefi ned. We can ignore this one exception,
though, as it will not come up in any of the problems we will be dealing with.
Our problem is that we need to get rid of the (0.004) multiplied by P on the right side.
Now, since any number^4 divided by itself is 1, we can eliminate that 0.004 if we divide
both sides by 0.004.
$1000
__0.004 

(P)(0.004)

__0.004

A calculator can easily handle the division on the left side. On the right we can divide 0.004

by 0.004 and get 1. Thus we get

$250,000  P(1)

and since anything multiplied by 1 is just itself

$250,000  P

which is the same as

P  $250,000.

And so, we can conclude that the amount that our retired friend needs in his account is

$250,000.

We can check this. Plugging in $250,000 for P into the simple interest formula, we get:

I  PRT

I  ($250,000)(0.048)(1/12)

I  $1,000

which is precisely what the interest was supposed to be. It worked!

Example 1.3.1 How much would you need to have in an investment account to earn

$2,000 simple interest in 4 months, assuming that the simple interest rate is 5.9%?

Following the approach we used above, we start with the simple interest formula, plugging

in $2,000 for I, 0.059 for R, and 4/12 for T. So:

I  PRT

$2,000  P(0.059)(4/12)

$2,000  P(0.01966667)

We then divide both sides of the equation by 0.01966667 to get:

$2,000

___________0.01966667 

P(0.01966667)

__0.01966667

P  $101,694.92

So we can conclude that you would need $101,694.92. It is a good idea to check this result

by using this value for P together with the R  0.059 and T  4/12 to make sure that the

interest actually is the desired $2,000.

In our first problem of this type, the number we had to divide by was a short decimal.

In Example 1.3.1, that was definitely not the case. Once we calculated 0.01966667, we

then had to write it down, and then enter “2000/0.01966667” into the calculator in order

to complete the calculation. Having to write this decimal down and then type it into the

calculator is a bit tedious, and it also invites the chance of making an error by accidentally

leaving out, mistyping, or switching digits.

Most calculators have a memory feature, which allows you to save a number into the

calculator memory and then recall it when you need it. Different calculator models will

have their memory keys labeled in a variety of different ways, and may require different

steps of keystrokes to save and then recall a stored number. You will need to check your

calculator’s owner’s manual, or ask your course instructor for the specific details of how to

do this on whichever calculator you are using.

1.3 Determining Principal, Interest Rates, and Time 23

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