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Word Problems/Per Year & For 1 Year



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?

I thank you for your reply.

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 ----------


I want to thank you for your reply.

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.

I thank you for your follow-up reply.

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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Scott A Wilson


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