# Finance Charge Per $100.00 #### KWF ##### Junior Member The calculation for determining the finance charge per$100.00 is determined by the following:

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

Since the denominator (amount finance) 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. Illustrated example:$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. 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.

#### Dr.Peterson

##### Elite Member
If the finance charge divided by the amount financed is the finance charge per $1.00. How does multiplying the finance charge/$1.00 by $100.00 equal the finance charge per$100.00? I do not understand how the $1.00 becomes$100.00.

Example: 3/4 * 6 = 18/4 not 18/24 or 0.75/1 * 6 = 4.5/1 not 4.5/6. Why doesn't the same reasoning apply to (finance charge/amount financed) * $100.00 equal (finance charge *$100.00)/amount financed?

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#### Dr.Peterson

##### Elite Member
Is this example, regarding what you have explained in your reply, correct?

3/4 * 6 = 18/4 = 9/2 or in your explanation 3/(4/6) = 3 divided by 2/3 = 9/2?
Yes, that is correct: division by a fraction (4/6) is equivalent to multiplication by the reciprocal (6/4), which in turn is equivalent to multiplying by the denominator (6) and dividing by the numerator (4), in either order.

But this does not explain the idea that 3/4 * 6 = 18/4 not 3/4 * 6/6 = 18/24 as does FC/AF * $100.00 = (FC *100)/AF not FC/AF *$100/$100. I've changed "2" above to "3", which you must have intended. The numerical example reflects the fact that multiplying by an integer (6) is the same as multiplying by that number over 1 (6/1), NOT by 6/6, which is equal to 1. Multiplying by 6/6 just results in a fraction equivalent to the original (18/24 = 3/4). In the same way, multiplying by$100 is not the same as multiplying by $100/$100.

#### KWF

##### Junior Member
Yes, that is correct: division by a fraction (4/6) is equivalent to multiplication by the reciprocal (6/4), which in turn is equivalent to multiplying by the denominator (6) and dividing by the numerator (4), in either order.

I've changed "2" above to "3", which you must have intended. The numerical example reflects the fact that multiplying by an integer (6) is the same as multiplying by that number over 1 (6/1), NOT by 6/6, which is equal to 1. Multiplying by 6/6 just results in a fraction equivalent to the original (18/24 = 3/4). In the same way, multiplying by $100 is not the same as multiplying by$100/$100. I still find this calculation confusing.$49/$200 *$100 = $0.245/$1.00 * $100 ls$24.50/1 not $24.50/$100. The calculation does not show how the denominator becomes $100.00. Why would anyone interpret$0.245/$1.00 *$100 as $24.50/$100? There are 24 1/2 cents per every dollar. I understand that much. I have always been told that whatever you do to the numerator you must perform the same calculation on the denominator so that it (the fraction) remains equivalent. $0.245/$1.00 = $24.50/$100 because both numerator and denominator are multiplied by 100.

I do thank you for your efforts in trying to explain this to me!

#### Dr.Peterson

##### Elite Member
I still find this calculation confusing. $49/$200 * $100 =$0.245/$1.00 *$100 ls $24.50/1 not$24.50/$100. The calculation does not show how the denominator becomes$100.00. Why would anyone interpret $0.245/$1.00 * $100 as$24.50/$100? There are 24 1/2 cents per every dollar. I understand that much. I have always been told that whatever you do to the numerator you must perform the same calculation on the denominator so that it (the fraction) remains equivalent.$0.245/$1.00 =$24.50/$100 because both numerator and denominator are multiplied by 100. I do thank you for your efforts in trying to explain this to me! The previous answer I referred to, from Oct 2, dealt with this exact question. Here is a link to the thread. I'll answer a little differently here. The calculation finds that the charge for$1.00 is $0.2450; that's your$0.245/$1.00. To find the charge for$100, we have to multiply that by 100 (since $100 is 100 times$1), and we get $24.50. That is the charge per$100, so that is what you are looking for.

This can be written as $24.50 per$100. The denominator, $100, that you expect is there! It's just in the wording rather than in the calculation. You could alternatively say that in order to find the ratio of charge to principal in this form, you multiply$49/$200 by$100/$100 (which is 1, so the meaning is unchanged, just as you said); this gives$24.50/$100. But the answer is not the whole fraction; "per$100" is taken as a unit describing the answer, and the numerator, $24.50, is the answer we want. In effect, when you are asked "what is the finance charge per$100", they are asking you to fill in the blank in "______/$100", and the answer is$24.50.

You seem to be obsessed with this, and things like this. If what I've said doesn't settle it for you, then you just have to do as we always do in dealing with the real world, and accept that this is how people talk about this subject.

#### Denis

##### Senior Member
KWF, you do know that % = per cent = per hundred (hundred = cent in French), right?

#### KWF

##### Junior Member
The previous answer I referred to, from Oct 2, dealt with this exact question. Here is a link to the thread.

I'll answer a little differently here.

The calculation finds that the charge for $1.00 is$0.2450; that's your $0.245/$1.00. To find the charge for $100, we have to multiply that by 100 (since$100 is 100 times $1), and we get$24.50. That is the charge per $100, so that is what you are looking for. This can be written as$24.50 per $100. The denominator,$100, that you expect is there! It's just in the wording rather than in the calculation.

You could alternatively say that in order to find the ratio of charge to principal in this form, you multiply $49/$200 by $100/$100 (which is 1, so the meaning is unchanged, just as you said); this gives $24.50/$100. But the answer is not the whole fraction; "per $100" is taken as a unit describing the answer, and the numerator,$24.50, is the answer we want.

In effect, when you are asked "what is the finance charge per $100", they are asking you to fill in the blank in "______/$100", and the answer is \$24.50.

You seem to be obsessed with this, and things like this. If what I've said doesn't settle it for you, then you just have to do as we always do in dealing with the real world, and accept that this is how people talk about this subject.

This will be my last reply to your response. I am not obsessed with this. Furthermore, I find your last comment unnecessary. This is not a place for personal opinion. I am just trying to better understand the calculation. Most professors with PhDs have a tone of arrogance in their character. I can detect that tone with you.

#### KWF

##### Junior Member
KWF, you do know that % = per cent = per hundred (hundred = cent in French), right?
...Etymologically, the word cent derives from the Latin word "centum. See Cent (currency)- Wikipedia
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