Solve A=P(1+r)^nc

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

Solve for P (complex solution)

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

Steps for Solving Linear Equation

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

$$P\left(1+r\right)^{nc}=A$$

The equation is in standard form.

$$\left(r+1\right)^{cn}P=A$$

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

$$\frac{\left(r+1\right)^{cn}P}{\left(r+1\right)^{cn}}=\frac{A}{\left(r+1\right)^{cn}}$$

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

$$P=\frac{A}{\left(r+1\right)^{cn}}$$

Solve for P

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

Steps for Solving Linear Equation

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

$$P\left(1+r\right)^{nc}=A$$

The equation is in standard form.

$$\left(r+1\right)^{cn}P=A$$

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

$$\frac{\left(r+1\right)^{cn}P}{\left(r+1\right)^{cn}}=\frac{A}{\left(r+1\right)^{cn}}$$

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

$$P=\frac{A}{\left(r+1\right)^{cn}}$$

Solve for A (complex solution)

$$A=P\left(r+1\right)^{cn}$$

Solve for A

$$A=P\left(r+1\right)^{cn}$$

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