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| Math Central | Quandaries & Queries |
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Question from Kenneth: Hello Math Central:
The calculation for determining the finance charge per $\$100.00$ (FC/100) is determined by the following: Example 1. 3/4 * 6 = 18/4 not 18/24 The 4 is not multiplied by the 6. 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. Kenneth |
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,
Penny
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
\[\frac12 \times \$49.00= \$24.50.\]
Penny
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