Math CentralQuandaries & Queries


Question from Kenneth:

Hello Math Central:

The calculation for determining the finance charge per $\$100.00$ (FC/100) is determined by the following:

Finance Charge/Amount financed * $\$100.00$ = the finance charge per $\$100.00$

Since the denominator (amount financed) is not multiplied by $\$100.00,$ how does the result equal the finance charge per $\$100.00?$ The numerator (finance charge) is the only amount multiplied by $\$100.00.$

Example 1. 3/4 * 6 = 18/4 not 18/24 The 4 is not multiplied by the 6.

Example 2. $\$49.00/\$200.00 * \$100.00$ If $\$49.00$ is divided by $\$200.00$ the result is $\$0.245/\$1.00.$ If $\$0.245/\$1.00 * \$100.00 = \$24.50/\$1.00$. This answer is not $\$24.50/\$100.00.$
How does the above equal the finance charge per $\$100.00$ when the denominator is not multiplied by $\$100.00?$

If the division is not used to indicate the $\$0.245$ per $\$1.00,$ the result becomes $\$49.00/\$200.00 * \$100.00 = \$4,900.00/\$200.00.$

I thank you for any helpful reply.


Hi Kenneth,

Let's look at your second example. The finance charge is $\$49.00$ and the amount financed is $\$200.00$ and hence

\[\frac{\mbox{Finance Charge}}{\mbox{amount finances}} = \frac{\$49.00}{\$200} = 0.245.\]

Since the units of the numerator and denominator are dollars they cancel and the result is a unit less number, 0.245. If you wish you can convert this to a percentage and think of 0.245 as 24.5%.

To obtain the finance charge per $\$100.00$ you need to multiply this fraction by $\$100.00$ to obtain

\[0.245 \times \$100.00 = \$24.5.\]

I hope this helps,

Kenneth wrote back

Hello Penny:

I want to thank you for the reply. However, I have a follow-up question that I want to ask.

How does $0.245\$100.00=\$24.5$ indicate $\$24.50$ per $\$100.00?$ I am still confused. I understand how the units cancel, but now does the result equal per $\$100.00.$

I thank you for any helpful reply that you can provide.

Perhaps this will help.

For every $\$200.00$ financed there is a finance charge of $\$49.00.$ Hence if the amount financed is half of that the finance charge will also be one half of the original finance charge. Thus if you finance $\$100.00$ the finance charge will be

\[\frac12 \times \$49.00= \$24.50.\]



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