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April 21st, 2010, 11:18 AM   #1
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Continuous compounding?

I cannot figure out a formula to work this word problem out.

''How long does it take $1000 to increase to $6750 if interest is compounded continuously at 5%?''

I have to show the work so if somebody could provide me a formula, I could take it from there. Thanks!
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April 21st, 2010, 02:08 PM   #2
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A suitable formula can be seen here.
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July 31st, 2010, 01:09 PM   #3
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Re: Continuous compounding?

Continuous compounding interest is the same thing as compounded interest, but it is compounded an infinite number of times at any given moment. The compounded interest formula is A=p(1+r/k)^kt, where "r" is interest, "k" is the number of times the interest is computed annually, and "t" is the number of years. Now, because continuous compounding happens an infinite number of times, the formula now becomes A=(1+r/infinity)^(infinity). Because infinity is not a number, we say that A=(1+r/n)^n, as "n" approaches infinity. And that's where "e" comes from. "e" is defined as "lim(1+1/n)^n as "n" approaches infinity. Therefore, the formula for continuous compounding is A=pe^kt. I hope this helps, I've never been very good at explaining things, but I think I covered all the main points.
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July 31st, 2010, 07:24 PM   #4
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Re: Continuous compounding?

A few comments come to mind, but I'll just stick with the less obnoxious ones:
a) that's usually a property of e, not its definition.
2) why bump this thread? Some sort of historical precedent from the life of Fermat?!?
d) "infinity is not a number" - I'm starting to think that you might be a sock puppet of deanmullen
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