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May 13th, 2018, 06:35 AM   #1
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problem with mathematical finance

I invested 6 years ago 30 thousand euros, 3 years ago the simple annual interest rate is 1.5% less than the original rate. If today I have 40 thousand euros, which was the original simple annual interest rate?

I've done this: 40000=30000+(30000*i*3)+[30000*3*(i-3/2i)]

so I have 45000i=10000 i=2/9 which is 22.222222...% but the correct answer should be 6.31%
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May 13th, 2018, 08:00 AM   #2
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The problem's wording is ambiguous. If, say, the original rate was 10%, is the reduced rate 8.5% or is it 9.85%?

To get the intended answer, solve 40000 = 30000 + 30000*3i% + 30000*3(i - 3/2)%, where "%" means "/100".

I find that i is exactly 227/36.
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May 13th, 2018, 08:10 AM   #3
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I'm sorry, I tried to translate the best I could. I'm Italian, so, I'm not a mother tongue I hope the wording problem didn't bother you
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May 13th, 2018, 08:26 AM   #4
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You're kinda close...but no ceegar!!

The total interest of 10,000 euros is calculated this way:
30000*(3*i) + 30000*(3*(i - .015)) = 10000
That'll end up with i = 227/3600 = .06305555555....; so 6.31% rounded.

Your only error is: [30000*3*(i-3/2i)] ; OK?
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May 13th, 2018, 08:27 AM   #5
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but could you explain to me why you solved it subtracting -3/2 without subtracting -3/2i? Isn't i lowered by 1.5%?
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May 13th, 2018, 08:38 AM   #6
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i - 3/2(i) = -1/2(i) which is evidently wrong.

If you're lowering a rate by 1.5%, then .015 is used in the ACTUAL calculation.
You could do it using 1.5, but then you'd need to divide by 100...same thing...
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May 13th, 2018, 08:42 AM   #7
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ah yes! of course. Thank you very much for your help!
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May 13th, 2018, 09:04 AM   #8
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Good...now you can apply for Head Interest Calculator
at the Royal Italian Bank of Commerce
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May 14th, 2018, 12:04 PM   #9
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ahahah, actually I don't like mathematical finance, well, at least I don't like it as much as I like every other argument in Math.
But unfortunately I've already chosen a finance school instead of a scientific one... what a big mistake I made
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