   SEARCH HOME Math Central Quandaries & 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. .......... 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     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.