p = x*(1 - (1+r)^-n)/r

In words: take the negative nth power of (1+r). Subtract from 1,
divide by r. 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? :confused:

C'mon... I know there are some mathematical genius's out there... and I don't want to fall off the new posts page :cool:

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.

Well, here's what I came up with:

-(1+r)^(1-rp/x)=n

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.

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) ÷ (log 2)

or

n = (ln 8) ÷ (ln 2)

n = 3

Mathcad gives the following solution: -ln(-(p*r-x)/x)/ln(1+r).

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

Dave