The Mathematics of Money

14 Chapter 1 Simple Interest

I  ($5,000)(.09)(0.5)

I  $225

So Sarai will pay back $5,000 + $225  $5,225.

So as we’ve just seen, when the term is given in months, we need to divide the number of

months by 12 to convert the term to years. In this first example, 6 divides into 12 nicely, but

of course, the same principle can be applied even when the numbers do not divide so neatly.

Example 1.2.2 Zachary deposited $3,412.59 in a bank account paying 5¼% simple

interest for 7 months. How much interest did he earn?

We can use the simple interest formula once again, plugging in P  $3,412.59 and R 

0.0525. Since the term is expressed in months, we divide 7/12 to get T  0.583333333.

I  PRT

I  ($3,412.59)(0.0525)(0.583333333)

I  $104.51

So Zachary earned $104.51 in interest.

This example raises an issue. Since 7/12 does not come out evenly, can it be rounded? In

general, the answer is no. In business it is accepted that a certain amount of rounding is

necessary, but a reasonable degree of accuracy is obviously expected. Too much rounding,

especially midway though a calculation, can cause results that are unacceptably far off of

the correct answer. In this text, rather than getting bogged down in determining how much

rounding is too much, we will follow the general rule that up until the final answer numbers

should be carried out to the full number of decimal places given by your calculator. In the

example above, the value was shown out to nine decimal places. Your calculator may have

more or fewer, but this will not be a problem. As long as you use the full precision of your

calculator, any differences will be small enough to be lost in the final rounding.

Fortunately, we can avoid the nuisance of having to write out or type in the entire

unrounded decimal. On most calculators, you can simply enter the whole expression into

the calculator at the same time:

Operation Result

3412.59*.0525*7/12 104.51056875

which rounds to the expected answer of $104.51.

We will use that approach in the next example.

Example 1.2.3 Yvonne deposited $2,719.00 in an account paying 4.6% simple

interest for 20 months. Find the total interest she earned.

I  PRT

I  ($2,719.00)(0.046)(20/12)

We evaluate the right side of this equation on the calculator:

Operation Result

2719*.046*20/12 208.4566667

Rounding this result we get:

I  $208.46

So Yvonne earned $208.46.

Depending on your prior math background, you may be uncomfortable with the fraction

(^20) ⁄ 12. You may have been told at some point that the numerator (the top) of a fraction must
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