The Mathematics of Money

24 Chapter 1 Simple Interest

Most Texas Instruments calculators have an “Ans” feature that recalls the result of the

last calculation. On most models it is located above the “(-)” key in the bottom row; you

can pull “Ans” onto your screen by hitting the “2nd” key followed by the “(-)”. If you are

using one of these models, you can perform the calculations of Example 1.3.1 as follows

(the number of decimal places displayed may vary depending on the model):

Operation Result

0.059*4/12 

2000/Ans 

0.01966667

101694.9153

While not absolutely necessary, using the calculator memory to store and recall values will

prove helpful in both this and future sections. If the instructions above are not sufficient to

figure out how to do this on the calculator model you are using, again, consult your owner’s

manual or your instructor for details on how to use your particular calculator.

Finding The Simple Interest Rate

Now let’s try our hand at the second scenario from the start of this section, where the inter-

est rate was the unknown. Jim borrowed $500 and paid $25 interest for a 90-day loan using

bankers’ rule. Plugging in the values we already know into the formula, we get:

I  PRT

$25  ($500)(R)(90/360)

which is similar to the previous situation, except that now the R lies between the numbers

on the right side. Fortunately, though, this doesn’t pose any real problem. Order does not

matter with multiplication; 2 times 3 times 5 is the same as 3 times 5 times 2, which is the

same as 5 times 2 times 3, and so on. Whichever way you multiply 2, 3, and 5, you get 30.

This means that in our equation it makes no difference where the R is, and so we can go

ahead on the right and multiply ($500)(90/360) to get $125, and so:

$25  $125(R).

We can now exploit the balance principle to get R alone by dividing both sides by $125:

$25

_____

$125



$125(R)

________

$125

and so

0.2  R

or

R  0.2

While this is technically correct, it does require some interpretation. Does this mean that

the interest rate is 0.2%? That seems awfully low.

Remember that before we plug an interest rate into the formula, we move the deci-

mal point two places to the left. And so when we solve for R, what we are getting is the

rate with the decimal already moved. While R  0.2 is technically a correct answer, the

fact is that we normally express interest rates as percents, and so we should do so here.

In order to turn this into a percent, we will need to move the decimal point two places

to the right.

R  0.2  20%.

and so the simple interest rate is 20%.

Note that, just as we inserted zeros where necessary to hold the place when moving to the

left (8% becomes .08 for example), we had to insert a zero here to hold the place on the right.