25-05-2005 16:34									#1
	Calculating Reverse Compund interest Support Apolyton, buy GURPS/ Alpha Centauri

Hi, can somebody help me with this very simple problem,

I have shares costing £3, in 6 years time they are worth £4.41. They have therefore increased by 1.41 over 6 years.

At a glance it might appear as if it's increased by 7.8% per year but that would be incorrect, as the compound effect means that in reality it's increased by 6.6% per year.

I can tell this by trial and error working it out.

But could somebody provide me with the formula to get their quicker

Cheers
Matt

	25-05-2005 16:44									#2
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If you assume it's compounded continuously, you get a simple differential equation, with a simple solution for the price of the share: S = S₀exp(r*t). That means r = ln(S/S₀)/t.

	25-05-2005 16:50									#3
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It would also be nice if you said what all of the symbols mean...

	25-05-2005 16:56									#4
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The natural meanings given the problem.

r is the interest rate, t is the time, S0 is the initial value, S is the final value.

	25-05-2005 17:56									#5
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quote: Originally posted by Ramo If you assume it's compounded continuously, you get a simple differential equation, with a simple solution for the price of the share: S = S0exp(r*t). That means r = ln(S/S0)/t.

In this case, you should assume an interval of one year. IOW, interest is added at the end of each year.

	25-05-2005 18:03									#6
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Does this equation allow for leap years?

	25-05-2005 18:56									#7
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quote: In this case, you should assume an interval of one year. IOW, interest is added at the end of each year.

I wasn't sure how many times he wanted interest compounded annually. Continuous compounding is so much cleaner.

If you're having annual compounding, S = So*(1 + r)^t. So r = (S/So)^(1/t) - 1.

	25-05-2005 21:25									#8
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quote: Originally posted by Ramo quote: In this case, you should assume an interval of one year. IOW, interest is added at the end of each year. I wasn't sure how many times he wanted interest compounded annually. Continuous compounding is so much cleaner.

While that looks good mathematically, nobody does that in real life.

	25-05-2005 21:26									#9
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We learned the equations for compound interest in 7th grade, but I don't remember them anymore).

	25-05-2005 21:29									#10
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FV = P(1 + r)ⁿ

FV = future value
P = starting principle
r = rate of return
n = time

edit: formula fixed

Last edited by chegitz guevara on 26-05-2005 at 04:23

	25-05-2005 21:55									#11
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quote: Originally posted by chegitz guevara FV = P(1 + r)n FV = future value P = starting principle r = rate of return n = time

The "n" should be an exponent, not a simple multiplier.

	25-05-2005 22:28									#12
	Avatar Enlargement: We've got the solution

Hi,
Thank you for your kind replies.

It was the annual I was after, i didnt see it in time before I left although i used the Continual compounding Ramo posted, which allowed me to get close enough to the Annual compounding by trail & error.
Cheers

	26-05-2005 04:05									#13
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Hey Boddingtons, I mean Worthingtons.

	26-05-2005 04:23									#14
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I don't think he's Bodds... no record in the name change log.

	26-05-2005 04:26									#15
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Can you say DL.

	26-05-2005 04:29									#16
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Was he banned?

	26-05-2005 04:30									#17
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Just cuz he has a similar name He doesn't behave like Spinky-poo.

	26-05-2005 04:34									#18
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Hi,
I'm not boddingtons. And I don't believe he is called that these days anyway?
I've made about 500 posts here, mainly in Civ 3 forums but some in here too. So maybe look at my history before you call me a DL. The name is simular though, I might change it at some point
Cheers

	26-05-2005 04:36									#19
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How was the game on Sunday?