Finance Charges on an installment loan is $49.00 and the amount financed is $200.00

KWF

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If the finance charge on an installment loan is $49.00 and the amount financed is $200.00, the finance charge per $1.00 is $0.245 ($49.00/$200.00). The finance charge per $100.00 is $24.50 ($49.00/$200 = $0.245/$1.00 * 100). What do these two amounts represent or indicate in regards to $1.00 and $100.00?

Is it for every $1.00 that is paid on the loan ($200.00), $0.245 is subtracted from it and the remainder is paid on the loan, and likewise, for every $100.00 that is paid on the loan ($200.00), $24.50 is subtracted from that amount and the remainder is paid on the loan?
 
If the finance charge on an installment loan is $49.00 and the amount financed is $200.00, the finance charge per $1.00 is $0.245 ($49.00/$200.00). The finance charge per $100.00 is $24.50 ($49.00/$200 = $0.245/$1.00 * 100). What do these two amounts represent or indicate in regards to $1.00 and $100.00?

Is it for every $1.00 that is paid on the loan ($200.00), $0.245 is subtracted from it and the remainder is paid on the loan, and likewise, for every $100.00 that is paid on the loan ($200.00), $24.50 is subtracted from that amount and the remainder is paid on the loan?

This question should really be put under Finance.

The finance charge is what you have to pay on the loan in addition to paying the principal. So it is not subtracted; it is in effect added. But in an installment loan, it is not handled directly; it is built into the payments -- that is, the sum of all the payments will be $249. And the ratio, $24.50/$100, is relative to the principal (amount financed), not the payment.

The formula for the payments is more complicated than you seem to be supposing. Have you learned anything about how loans are calculated? One way to do it involves calculating the ratio you are asking about, and looking it up in a table.
 
If the finance charge on an installment loan is $49.00 and the amount financed is $200.00, the finance charge per $1.00 is $0.245 ($49.00/$200.00). The finance charge per $100.00 is $24.50 ($49.00/$200 = $0.245/$1.00 * 100). What do these two amounts represent or indicate in regards to $1.00 and $100.00?

Is it for every $1.00 that is paid on the loan ($200.00), $0.245 is subtracted from it and the remainder is paid on the loan, and likewise, for every $100.00 that is paid on the loan ($200.00), $24.50 is subtracted from that amount and the remainder is paid on the loan?
Your questions are quite strange...

IF the loan is over 1 year (as example) with monthly payments,
then $249 will be the amount repaid: means 249/12 = $20.75

It'll look like this:
Code:
MONTH PAYMENT INTEREST BALANCE
   0                    200.00
   1  -20.75    7.08    186.33
   2  -20.75    6.60    172.18
.....
  11  -20.75    1.39     20.05
  12  -20.75     .70       .00
     -------   -----
     -249.00   49.00
Rate turns out to be ~42.48% APR cpd. monthly.
However, numeric method required to calculate it.
 
"Finance charge" is defined legally in the U.S. It is, as everyone who really understands the issue knows, the cause of "payday lending." I have had long discussions with both the FDIC and the OCC, two of the major regulators of banks in the U.S., about why the legal definition of "finance charge" under federal law effectively abandons poor people who need short-term, low-amount loans to the absent mercies of the totally unscrupulous. No legitimate business wants the opprobrium that federal law will visit on those who seek to provide a three-day loan of $600 to a person of dubious creditworthiness at anything close to no loss. An interest charge of 10% on such a loan would result in revenue of less than

\(\displaystyle 0.1 * $600 * \dfrac{3}{365} < 0.1 * $600 * \dfrac{3}{360} = 50 \text { cents,}\)

way, way below the clerical cost to book the loan, let alone cover the risk of loss on the loan. It is safer and more profitable under federal law to lend to people who have the debt capacity to borrow in the tens of thousands and reject out of hand people who want small amounts for a few days.

"Finance charges" are an artifact of law that can be explicated only in terms of statutory and regulatory language. Common sense, math, and morality have nothing to say about a "Schumer box." Chuck Schumer created, almost certainly unknowingly, a new and legal type of loan shark, the "payday lender," out of total ignorance of the economics of lending: there are fixed costs of lending that interest at any seemingly reasonable rate cannot possibly cover for short-term, low-balance loans. (The cynics may say that Schumer was working to benefit a new breed of loan sharks, but I know of no evidence to that effect, nor do I think that loan sharks were clever enough to anticipate the implications of the Schumer box.)
 
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This question should really be put under Finance.

The finance charge is what you have to pay on the loan in addition to paying the principal. So it is not subtracted; it is in effect added. But in an installment loan, it is not handled directly; it is built into the payments -- that is, the sum of all the payments will be $249. And the ratio, $24.50/$100, is relative to the principal (amount financed), not the payment.

The formula for the payments is more complicated than you seem to be supposing. Have you learned anything about how loans are calculated? One way to do it involves calculating the ratio you are asking about, and looking it up in a table.

The calculation for determining the finance charge per $100.00 is as follows: finance charge/amount financed * 100, or I have seen it expressed as financed charge divided by amount financed/100. Why is the dollar sign omitted from the 100? Wouldn't it be more accurate to express these with the dollar sign on the 100.00 as finance charge/amount financed * $100 and financed charge divided by amount financed/$100?

Here some examples: finance charge is $49.00; amount financed is $200. Would these examples be more accurate: $49.00/$200.00 * $100.00 and likewise $49.00 divided by $200/$100.00 In these examples, one can see how the dollar units cancel.
 
The calculation for determining the finance charge per $100.00 is as follows: finance charge/amount financed * 100, or I have seen it expressed as financed charge divided by amount financed/100. Why is the dollar sign omitted from the 100? Wouldn't it be more accurate to express these with the dollar sign on the 100.00 as finance charge/amount financed * $100 and financed charge divided by amount financed/$100?

Here some examples: finance charge is $49.00; amount financed is $200. Would these examples be more accurate: $49.00/$200.00 * $100.00 and likewise $49.00 divided by $200/$100.00 In these examples, one can see how the dollar units cancel.

First, I should mention that my comment about the formula being complicated was really about figuring out what the finance charge would be given an interest rate, which was never part of your question. Once you know the finance charge, you can easily find the payments, or vice versa.

But as to what you are asking about here, the finance charge is stated as a charge (in dollars) per $100 of amount financed, so you do indeed divide the amount financed by $100, not just 100, before dividing the finance charge by that (dimensionless) result. This makes the result a number of dollars, e.g. "$9", so that the whole ratio, "$9 per $100",is dimensionless as it should be. But I can imagine someone saying otherwise and not being entirely nonsensical. The real finance people here may have more to say about how it is usually stated.

You appear to be referring to some particular explanation of it that you have seen, rather than necessarily something standard. Is there a specific source you can refer us to? I searched for a textbook explanation (as opposed to somebody answering a question on a help site), and found, for example, one (a powerpoint from a publisher) that says

Find the interest per $100 financed; divide the finance charges including interest by the amount financed and multiply by $100.

That sounds like it agrees with you (and me). Here is an actual textbook that says the same:

Finance Charge per $100 of Amount Financed = Finance Charge/Amount Financed * $100

So, what is your source that says otherwise?
 
First, I should mention that my comment about the formula being complicated was really about figuring out what the finance charge would be given an interest rate, which was never part of your question. Once you know the finance charge, you can easily find the payments, or vice versa.

But as to what you are asking about here, the finance charge is stated as a charge (in dollars) per $100 of amount financed, so you do indeed divide the amount financed by $100, not just 100, before dividing the finance charge by that (dimensionless) result. This makes the result a number of dollars, e.g. "$9", so that the whole ratio, "$9 per $100",is dimensionless as it should be. But I can imagine someone saying otherwise and not being entirely nonsensical. The real finance people here may have more to say about how it is usually stated.

You appear to be referring to some particular explanation of it that you have seen, rather than necessarily something standard. Is there a specific source you can refer us to? I searched for a textbook explanation (as opposed to somebody answering a question on a help site), and found, for example, one (a powerpoint from a publisher) that says
Find the interest per $100 financed; divide the finance charges including interest by the amount financed and multiply by $100.

That sounds like it agrees with you (and me). Here is an actual textbook that says the same:
Finance Charge per $100 of Amount Financed = Finance Charge/Amount Financed * $100

So, what is your source that says otherwise?


I have attached a copy from an old high school textbook that indicates otherwise, without the dollar sign ($) with the 100. See the bottom of the page. I think older textbooks did not use the dollar sign for the calculation, but I do not have any proof to support this belief. It is something that is curious to me, though.


I am also curious to know why does multiplying by 100 or $100.00 represent the finance charge per $100.00 when the denominator is not multiplied by $100.00 as well.

Here is an example: $49.00 represents the finance charge and $200.00 represents the amount financed. The calculation would appear as $49.00/$200.00 * $100.00 = $24.50 the finance charge per $100.00. What I am indicating is that the $200.00 is not multiplied by $100.00 as the $49.00 is, but the result is $24.50 per $100.00, $24.50/$10000. I used a proportion to see how this would appear with $100.00.

$49.00/$200.00? = ?/$100.00

When solving for the unknown amount, the calculation becomes $49.00 * $100.00 = ? * $200.00. After dividing both sides by $200.00 the calculation becomes ($49.00 * $100.00)/$200 = ? This calculation is the one shown above for determining the finance charge per $100.00: $49.00/$200.00 * $100.00. This finance charge per $100.00 calculation appears to be a part of the proportion calculation. I hope you understand what I have explained here.
 

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I have attached a copy from an old high school textbook that indicates otherwise, without the dollar sign ($) with the 100. See the bottom of the page. I think older textbooks did not use the dollar sign for the calculation, but I do not have any proof to support this belief. It is something that is curious to me, though.

I'd say the book is just ignoring units in the calculation. That's not uncommon; when you calculate, say, E = mc^2, you usually just put in the numbers, knowing that if you used the right units going in, you'll get the right units coming out. It may well be that more recent textbooks try to be more mathematically particular, showing why things are the way they are.

I am also curious to know why does multiplying by 100 or $100.00 represent the finance charge per $100.00 when the denominator is not multiplied by $100.00 as well.

Here is an example: $49.00 represents the finance charge and $200.00 represents the amount financed. The calculation would appear as $49.00/$200.00 * $100.00 = $24.50 the finance charge per $100.00. What I am indicating is that the $200.00 is not multiplied by $100.00 as the $49.00 is, but the result is $24.50 per $100.00, $24.50/$10000. I used a proportion to see how this would appear with $100.00.

$49.00/$200.00? = ?/$100.00

When solving for the unknown amount, the calculation becomes $49.00 * $100.00 = ? * $200.00. After dividing both sides by $200.00 the calculation becomes ($49.00 * $100.00)/$200 = ? This calculation is the one shown above for determining the finance charge per $100.00: $49.00/$200.00 * $100.00. This finance charge per $100.00 calculation appears to be a part of the proportion calculation. I hope you understand what I have explained here.

If you multiply both the numerator and the denominator by the same thing, you're just multiplying by 1 -- the value is left unchanged. Sometimes (as in simplifying a fraction), that's what you want to do; but not in a case like this. You want to get a new number that has a new meaning, not to get back the same number you had. That is, (49*100)/(200*100) is the same number as 49/200, namely 0.245.

On the other hand, in a sense you are multiplying by $100 in both places -- but one of them is remaining as part of the unit!

In your example, you want the finance charge per $100. In the form you show, you divide $49 by $200 to get a ratio, and then you multiply by $100 per $100! That is, you multiply by $100, and the result is the number you get, per $100. The denominator is in the unit.

This is identical to what you do in converting a fraction to a percentage. The word "percent" means "per 100"; the 100 is in the name of the unit. When you say 75%, you mean 75/100, or 75 per 100. So when you multiply 3/4 by 100 to get a percentage, you are really multiplying by 100%, that is, 100 per 100 (which is a form of 1, so that the result means the same as the original fraction, but in a different form):

3/4 * 100% = (3/4 * 100)% = 75%

or, in words,

3/4 * 100 per 100 = (3/4 * 100) per 100 = 75 per 100

Now, if you actually "finished" the work by dividing by 100, you'd get 0.75. This is how we convert a percentage back to a decimal or a fraction. Then you have just a number, not a percentage. That is, when we say 75%, we mean 75/100, but we've left that division undone, because it is the meaning of the unit, "%".

Note that your finance charge is, in fact, 0.245 (per dollar), which is 25.5%: 25.5 per hundred.
 
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