Solve S=P(1+r)^n

$$S = P ( 1 + r ) ^ { n }$$

Solve for P (complex solution)

$$\left\{\begin{matrix}P=\frac{S}{\left(r+1\right)^{n}}\text{, }&n=0\text{ or }r\neq -1\\P\in \mathrm{C}\text{, }&S=0\text{ and }r=-1\text{ and }n\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$P\left(1+r\right)^{n}=S$$

The equation is in standard form.

$$\left(r+1\right)^{n}P=S$$

Divide both sides by \left(1+r\right)^{n}.

$$\frac{\left(r+1\right)^{n}P}{\left(r+1\right)^{n}}=\frac{S}{\left(r+1\right)^{n}}$$

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

$$P=\frac{S}{\left(r+1\right)^{n}}$$

Solve for P

$$\left\{\begin{matrix}P=\frac{S}{\left(r+1\right)^{n}}\text{, }&r>-1\text{ or }\left(Denominator(n)\text{bmod}2=1\text{ and }r<-1\right)\\P\in \mathrm{R}\text{, }&S=0\text{ and }r=-1\text{ and }n>0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$P\left(1+r\right)^{n}=S$$

The equation is in standard form.

$$\left(r+1\right)^{n}P=S$$

Divide both sides by \left(1+r\right)^{n}.

$$\frac{\left(r+1\right)^{n}P}{\left(r+1\right)^{n}}=\frac{S}{\left(r+1\right)^{n}}$$

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

$$P=\frac{S}{\left(r+1\right)^{n}}$$

Solve for S (complex solution)

$$S=P\left(r+1\right)^{n}$$

Solve for S

$$S=P\left(r+1\right)^{n}$$

$$\left(r<-1\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(r=-1\text{ and }n>0\right)\text{ or }r>-1$$