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I have some problems understanding a question in a math class test for 10 year olds.

The question is:

Someone pays in 200€ to a bank. The interest rate is 3.75%. Some time later, he looks at the account balance and he sees that there are 235€ now. How much time passed?

I would calculate this using logarithms, but the interesting part here is that they don't even know square roots, not to mention logarithms.

Is there any easy way to calculate this without logarithms that I overlooked?

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Per year? Compounded how often? There shouldn't be a way to do this without logarithms (in some sense) unless the numbers come out cleanly, and they don't seem to. –  Qiaochu Yuan Dec 7 '10 at 8:50
    
You can also try by compounding and building up the geometric sequence element by element. They still learn to multiply, do they? –  Raskolnikov Dec 7 '10 at 8:50
    
I guess it's per year, but there's no information about this in the exercise. I don't remember the exact exercise, but the numbers do not come out cleanly anyway. Yes, they just learned to multiply and they do percent calculations at the moment (+10%, How much is 34 apples from 200,...). –  leoluk Dec 7 '10 at 8:59
    
Do they have to come out cleanly? Maybe if you round them off, it's okay. Besides, what numbers in reality do come cleanly out? I bet you the teacher asked his pupils to compute if his raise on his paycheck is correct. ;p –  Raskolnikov Dec 7 '10 at 9:04

1 Answer 1

up vote 4 down vote accepted

It depends on whether the interest is simple or compound. If the interest is simple, you look at the fact the the 35C gain is a gain of 17.5%. Then, 17.5% divided by 3.75% is 4 and two third years (assuming the interest is 3.75% per year). If the interest is compound, I see no other way then using logarithms producing an answer of about 4.38 years. If this is meant to be an easy problem, they are probably assuming simple interest since 4 and two third years is not a very complicated answer.

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2  
$(1+x)^n \approx 1+nx$, these kids nowadays, they learn Taylor series approximations before even knowing how to take a logarithm. Don't believe them in 10 years when they'll tell you they don't understand Taylor series. ;p –  Raskolnikov Dec 7 '10 at 9:14
    
I had a good laugh, @Ras. Thanks for making my day. :) –  J. M. Dec 7 '10 at 14:44

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