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QUESTION: Hello:

If the finance charge is $35.00 of the amount financed of $700.00, what is the finance charge per $100.00 of the amount financed?

[Finance charge is $35.00 and amount financed is $700.00.]

Solution: ($35.00/$700.00) X $100 = ($0.05/1) X 100 = finance charge of $5.00 per $100.00 of the amount financed.

($0.05/1) equals finance charge of $0.05 per $1.00 of the amount financed. Multiplying $0.05/1 by 100 equals finance charge of $5.00 per $100.00 of the amount financed.

Or multiply $35.00 first by $100.00 and then divide by $700.00 as in the following:

($35.00 X $100)/ $700.00 = $3500.00/700 = finance charge of $5.00 per $100.00 of the amount financed.

What would the following calculation indicate by multiplying $700.00 by $100 first as in $35/($700.00 X $100) = 35/$70,000 = 1/$0.0005? What does 1/$0.0005 indicate?

I thank you for your reply.

ANSWER: The order of multiplication does not matter, because of the commutative property of multiplication.

However, $35/($700×$100) is incorrect. You want to convert $100 into the equivalent finance charge, so $100 belongs in the numerator and is multiplied by the rate.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for the reply.

Which is the rate? You indicated the following: " You want to convert $100 into the equivalent finance charge, so $100 belongs in the numerator and is multiplied by the rate."

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I noticed an error in my first message: 1/$0.0005 should be 0.0005/$1.00 if I'm not mistaken. But i still do not know what this amount indicates.

I thank you for your follow-up reply.

The rate is the finance charge per amount borrowed. The more you borrow, the greater the finance charge.

You were charged $35 on a $700 loan, so the rate is (35 dollars-charged)/(700 dollars-borrowed).

Now divide both numerator and denominator by 700:

(35 dollars-charged)/(700 dollars-borrowed) is equal to (0.05 dollar-charged)/(1 dollar-borrowed).

The solution they gave showed that you can use either form of the rate, 35/700 or 0.05/1, and get the same answer:

(100 dollars-borrowed) · (0.05 dollar-charged)/(1 dollar-borrowed) = 5 dollars-charged

(100 dollars-borrowed) · (35 dollars-charged)/(700 dollars-borrowed) = 5 dollars-charged

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You asked "What would the following calculation indicate by multiplying $700.00 by $100 first as in $35/($700.00 X $100)" = 35/$70,000 ?"

This equation shows DIVIDING by $100, not multiplying by $100. That's why you got 0.0005/$1, which is incorrect.

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