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# Word Problems/Per Year & For 1 Year

Question
QUESTION: Hello:

What is the difference between interest per year and interest for 1 year?

Here is an example:  6%/year X \$600.00 = \$36/year (\$36 per year)

1/4 of one year of this amount is one-fourth year times \$36.00/year.

The amount is \$9.00 for one fourth year even though the year units have canceled. It's not \$9.00 for 1/4 per year is it?

Can you clarify?

ANSWER: The interest rate for 1 year is the total interest paid in that year.
The interest per year is computed by dividing the interest rate for 1 year into smaller blocks and multiplying it together.

For example, 6% per year is really .5% per month and calculated 12 times during the year.
The 6% interest rate for one year really is 6.168% interest rate when you compute (1.005)^12 - 1.

If it was 6% per year computed quarterly, divide this by 4 and raise it to the 4 to get the effect.  That is, since 1.5% is 1/4 of 6%, 1.15^4 - 1 is the actual interest for 1 year.
It turns out to really be 6.136% per year.

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

QUESTION: Hello:

I am referring to simple interest.  Is what you indicated in your first reply for simple interest?  It appears to be what occurs with compound interest.

In that case, the answer is correct.  As far as the question at the start, they both mean the same thing.  If the interest rate is 6% simple interest, then that could be 3% simple interest twice a year, 1.5% simple interest 4 times a year, .5% 12 times a year, or anything else where the interest times the number of times per year is 6%.

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 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the reply!

Word Problems

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#### Scott A Wilson

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