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# Word Problems/Amount Financed Per \$100

Question
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?

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.

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.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the clarification and reply!

Word Problems

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#### Janet Yang

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