The Mathematics of Money

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

We can also check this result:

I = PRT

I = ($500)(0.20)(90/360)

I = $25

Example 1.3.2 Calculate the simple interest rate for a loan of $9,764.55 if the term

is 125 days and the total required to repay the loan is $10,000.

First we need to fi nd the interest by subtracting. The total interest is $10,000  $9,764.55 =

$235.45. Also, recall that since nothing was said otherwise, we assume the exact method with

365 days.

Plugging values into the formula gives:

I = PRT

$235.45 = ($9,764.55)R(125/365)

$235.45 = ($3,344.02397260)R

To solve for R, we divide both sides by 3344.02397260. As in Example 1.3.2 it is probably

easiest to take advantage of your calculator’s memory to do this. In any case, though, divid-

ing through we get:

R = 0.0704091842

Moving the decimal two places to the right, we can state the rate as 7.04091842%.

It is not usually necessary to carry the fi nal answer out to this many decimal places, though.

There is no absolute rule about how many places to use, but in most situations two or at

most three decimal places in the fi nal percent is acceptable. For our purposes in this text, two

decimal places will be fi ne, so we conclude that the interest rate is 7.04%.

Finding Time

Lastly, let’s consider the third scenario, where time was the unknown. Maria deposited

$9,750 in a savings account that pays 5^1 ⁄ 4 % simple interest and wanted to know how long

it would take for her account to grow to $10,000.

We proceed as before:

I = PRT

$250 = ($9,750)(0.0525)(T)

$250 = $511.875(T)

_________$250

$511.875

= $511.875(T)____________

$511.875

T = 0.4884004884

This answer seems like it must be wrong, since it makes no sense. T = 0.4884004884?

What does that tell us?

To make sense of this, we need to remind ourselves that as long as the interest rate is a

rate per year (which we assume unless explicitly told otherwise), the time in our formula

must also be expressed in years. So what this equation is telling us is that the required time

would be 0.4884004884 years. That would be a bit less than half a year, which does seem

reasonable. Leaving the answer in this form, though, is probably going to be unacceptable

to most people. “A bit less than half a year” is a tad too vague.

When talking about periods of time less than a year, instead of using messy decimals we

usually just use smaller units of time, such as months or days. So we need to convert this

decimal number of years into months or days.

To convert it into months, let’s recall how we went about things in the other direction.

When we were given a term in months, we divided by 12 to get the term in years. So:

years  _______months

12

1.3 Determining Principal, Interest Rates, and Time 25