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Topic: Interesting interest (Read 562 times) |
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Noke Lieu
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Interesting interest
« on: Mar 10th, 2009, 9:18pm » |
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A new bank has opened in Cuckooland, where interest is calculated and added daily.
It lets you name your compound interest rate (under 20%) for deposits. The only catch is that it'll offer you double that rate to take it as simple interest instead.
As expected, Simple interest starts off winning.
After how many days does it pay better to have chosen Compound interest?
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| « Last Edit: Jun 30th, 2009, 10:37pm by Noke Lieu » |
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towr
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Re: Interesting
« Reply #1 on: Mar 11th, 2009, 2:23am » |
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The interest rate is per day? Then after ~7.7 days compound is better than simple. Unless you withdraw your deposit each day and then (have a friend) deposit it again 
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Immanuel_Bonfils
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Re: Interesting
« Reply #2 on: Mar 11th, 2009, 5:43pm » |
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Seems the rate is less than 20% and not 20%... (I don't know why)
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Noke Lieu
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Re: Interesting
« Reply #3 on: Mar 11th, 2009, 6:14pm » |
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Towr... I have a different answer.
Either I've completely lost the plot (given the events of this morning, entirely plausible), or what I was expecting to ask wasn't quite what you've answered.
Even if I plug in to Excel (oh dear)
100 . 100
=a1*1.1 . 120
=a2*1.1 . 140
at day 15 it's 379.75 vs 380....
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towr
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Re: Interesting
« Reply #4 on: Mar 12th, 2009, 2:04am » |
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on Mar 11th, 2009, 6:14pm, Noke Lieu wrote:Even if I plug in to Excel (oh dear)
100 . 100
=a1*1.1 . 120
=a2*1.1 . 140 |
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I have no idea what that means. *is total excel newb*
I did 1.20n vs 1+0.40*n, since in the limit 20 is the highest interest rate you can get, and a higher interest rate is always better to get than a lower one.
n=7 : 3.5832 vs 3.8
n=8 : 4.2998 vs 4.2
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Noke Lieu
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Re: Interesting
« Reply #5 on: Mar 12th, 2009, 3:59pm » |
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well, yeah. That's what that does, except it's
(1.1)n vs (1.2)n
Yes, for taking 20%, 7.7 days is what I get too.
But that's only for 20%.
at 10%, it's much longer.
Why not takethe 20%? who knows. It's cuckooland, after all.
perhaps somewhere in the fine print, it says we take as many fingers as you claim in percent interest...
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towr
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Re: Interesting
« Reply #6 on: Mar 12th, 2009, 4:14pm » |
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on Mar 12th, 2009, 3:59pm, Noke Lieu wrote:Yes, for taking 20%, 7.7 days is what I get too.
But that's only for 20%.
at 10%, it's much longer. |
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At 1% it is much longer still. And at 0.1% even longer. There isn't really a limit to it. 
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Noke Lieu
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Re: Interesting
« Reply #7 on: Mar 12th, 2009, 5:26pm » |
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hence, what I was after was the solution to
(1+I/100)n = (1 + 2I/100)n, giving n in terms of I, or somesuch.
as I approches 0, compound interest wins out as In approaches...?
I was trying to dust off how to use logs, having not done them formally in years and years. and failing.
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| « Last Edit: Mar 12th, 2009, 5:35pm by Noke Lieu » |
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towr
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Re: Interesting
« Reply #8 on: Mar 13th, 2009, 1:06am » |
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on Mar 12th, 2009, 5:26pm, Noke Lieu wrote:| I was trying to dust off how to use logs, having not done them formally in years and years. and failing. |
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On this problem, that's hardly a surprise. You need the Lambert W function, rather than logs.
You can get decent approximations without it, but even that goes beyond mere logarithms. Such as perhaps using a Taylor expansion to approximate (1+I/100)n for small I.
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