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.
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