My Math Forum problem with mathematical finance

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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*(i-3/2i)] 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: 20,274 Thanks: 1959 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. Thanks from FreeeZy00
 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: 13,954 Thanks: 987 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? Thanks from FreeeZy00
 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: 13,954 Thanks: 987 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... Thanks from FreeeZy00
 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: 13,954 Thanks: 987 Good...now you can apply for Head Interest Calculator at the Royal Italian Bank of Commerce Thanks from Joppy
 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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