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Word Problems/Interest Rates

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Question
Hello:

To determine interest a loan for a period other than one year use the following:

$400.00 X 5% X 2 1/2 years.

The interest on a loan is in proportion to the time.

How would a proportion be used to represent what is indicated above, that is, "The interest ... is in proportion to the time"?

Would the following be correct?

($50/$20 X $20) = (2 1/2 X 1 year)

I thank you for your reply.

Answer
First note that you are calculating simple interest, not compound interest. That is, the interest is based on the principal of the loan, not on any accrued interest.

Let P be the principal (loan amount), r the interest rate per unit of time, t the number of time units, and i the interest earned, then
The interest earned varies directly with principal, rate, and time:
 i = Prt
Normally, the unit of time is one year.


Suppose the principal is $400, the rate is 5% per year, and the period is 2.5 years.
 i = $4000.052.5 = $50
The interest over 2.5 years is $50.  

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Janet Yang

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Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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