Question

R = P (C) / 1 - (1+C) ^ -n

steps to solve for n?

Answer 1

What is R, P, C?

Answer 2

\[R=\frac{P}{1-(1+C)^{-n}} \rightarrow \frac{1}{R}=\frac{1-(1+C)^{-n}}{P}\]\[\rightarrow \frac{P}{R}=1-(1+C)^{-n} \rightarrow (1+C)^{-n}=1-\frac{P}{R}=\frac{R-P}{R}\]\[\rightarrow \log (1+C)^{-n}=\log \frac{R-P}{R}\]\[\rightarrow -n \log (1+C)=\log \frac{R-P}{R}\rightarrow n \log (1+C)=\log \frac{R}{R-P}\]\[\rightarrow n =\frac{\log \frac{R}{R-P}}{\log (1+C)}\]