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Rearrange this formula to solve for n (no, its not my homework lol)

Asked Aug 22, 2006, 02:22 PM — 6 Answers
P = x*(1 - (1+r)^-n)/r

In words: take the negative nth power of (1+r). Subtract from 1,
Divide by are. This gives the ratio of p to x.

I need to be able to solve for n.

Can someone help me with creating a formula out of this to solve for n?

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6 Answers
DrJ's Avatar
DrJ Posts: 1,344, Reputation: 1758
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#2

Aug 22, 2006, 04:08 PM
C'mon... I know there are some mathematical genius's out there... And I don't want to fall off the new posts page
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worthbeads's Avatar
worthbeads Posts: 569, Reputation: 280
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#3

Aug 22, 2006, 05:16 PM
This one's a tough one. I'm not exactly sure about the answer, but if it helps, I think p=-x, but I would check that if I were you.
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DrJ's Avatar
DrJ Posts: 1,344, Reputation: 1758
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#4

Aug 22, 2006, 06:02 PM
Well, here's what I came up with:

-(1+r)^(1-rp/x)=n
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dmatos's Avatar
dmatos Posts: 204, Reputation: 129
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#5

Aug 22, 2006, 06:27 PM
You have to use logarithms to "undo" powers. This is what I get:

N = ln(1-rp/x)/ln(1+r)

Where ln is the natural logarithm. A logarithm in any base would work, as long as you used the same top and bottom, but because of the special features of log(base e), ln is often used for this type of thing.
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rudi_in's Avatar
rudi_in Posts: 252, Reputation: 224
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#6

Aug 22, 2006, 06:47 PM
I agree that you will have to use logs to solve this one.

A quick verification on the calculator to show that this does work could be as follows...


2ⁿ = 8

N = (log 8)
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DaveS002's Avatar
DaveS002 Posts: 2, Reputation: 1
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#7

Oct 28, 2006, 06:32 AM
Mathcad gives the following solution: -ln(-(p*r-x)/x)/ln(1+r).

Of course p, are, and x will have to be in proper bounds in order to take the ln.

Dave
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