Solve V=P(1+i)^N

$$V = P ( 1 + i ) ^ { N }$$

Solve for P

$$P=\frac{V}{\left(1+i\right)^{N}}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$P\left(1+i\right)^{N}=V$$

The equation is in standard form.

$$\left(1+i\right)^{N}P=V$$

Divide both sides by \left(1+i\right)^{N}.

$$\frac{\left(1+i\right)^{N}P}{\left(1+i\right)^{N}}=\frac{V}{\left(1+i\right)^{N}}$$

Dividing by \left(1+i\right)^{N} undoes the multiplication by \left(1+i\right)^{N}.

$$P=\frac{V}{\left(1+i\right)^{N}}$$

Solve for N

$$\left\{\begin{matrix}N=\frac{8\pi n_{1}i}{2\ln(2)+\pi i}+\frac{4\ln(\frac{V}{P})}{2\ln(2)+\pi i}\text{, }n_{1}\in \mathrm{Z}\text{, }&V\neq 0\text{ and }P\neq 0\\N\in \mathrm{C}\text{, }&V=0\text{ and }P=0\end{matrix}\right.$$