I need help solving for n

Question

Original equation:

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

Sooo... I got this far. I'm not sure this is right

1 / -(1+r)ⁿ = ((r*V) / P)-1

n=????

Answer 1

p = rV / [1 - (1 + r)^-n]

Let us take this step by step.

p/(rV) = 1 / [1 - (1 + r)^-n]

rV/p = 1 - (1 + r)^-n

1 - rV/p = (1 + r)^-n

log(1 - rV/p) = -n log(1 + r)

n = -log(1 - rV/p) / log(1 + r)

You can simplify this a little more if you wish. Work with any base for the logs, as long as you use the same base in both logs,