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May 13th, 2018, 07:35 AM  #1 
Newbie Joined: May 2018 From: Italy Posts: 5 Thanks: 0  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*(i3/2i)] so I have 45000i=10000 i=2/9 which is 22.222222...% but the correct answer should be 6.31% 
May 13th, 2018, 09:00 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,887 Thanks: 1836 
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. 
May 13th, 2018, 09:10 AM  #3 
Newbie Joined: May 2018 From: Italy Posts: 5 Thanks: 0 
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

May 13th, 2018, 09:26 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,486 Thanks: 950 
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*(i3/2i)] ; OK? 
May 13th, 2018, 09:27 AM  #5 
Newbie Joined: May 2018 From: Italy Posts: 5 Thanks: 0 
but could you explain to me why you solved it subtracting 3/2 without subtracting 3/2i? Isn't i lowered by 1.5%?

May 13th, 2018, 09:38 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,486 Thanks: 950 
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... 
May 13th, 2018, 09:42 AM  #7 
Newbie Joined: May 2018 From: Italy Posts: 5 Thanks: 0 
ah yes! of course. Thank you very much for your help! 
May 13th, 2018, 10:04 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,486 Thanks: 950 
Good...now you can apply for Head Interest Calculator at the Royal Italian Bank of Commerce 
May 14th, 2018, 01:04 PM  #9 
Newbie Joined: May 2018 From: Italy Posts: 5 Thanks: 0 
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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