Solve A=P(1+r/n)^nt

$$A = P ( 1 + \frac { r } { n } ) ^ { n t }$$

Solve for P (complex solution)

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

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{n}{n}.

$$A=P\left(\frac{n}{n}+\frac{r}{n}\right)^{nt}$$

Since \frac{n}{n} and \frac{r}{n} have the same denominator, add them by adding their numerators.

$$A=P\times \left(\frac{n+r}{n}\right)^{nt}$$

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

$$P\times \left(\frac{n+r}{n}\right)^{nt}=A$$

The equation is in standard form.

$$\left(\frac{n+r}{n}\right)^{nt}P=A$$

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

$$\frac{\left(\frac{n+r}{n}\right)^{nt}P}{\left(\frac{n+r}{n}\right)^{nt}}=\frac{A}{\left(\frac{n+r}{n}\right)^{nt}}$$

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

$$P=\frac{A}{\left(\frac{n+r}{n}\right)^{nt}}$$

Solve for P

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

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{n}{n}.

$$A=P\left(\frac{n}{n}+\frac{r}{n}\right)^{nt}$$

Since \frac{n}{n} and \frac{r}{n} have the same denominator, add them by adding their numerators.

$$A=P\times \left(\frac{n+r}{n}\right)^{nt}$$

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

$$P\times \left(\frac{n+r}{n}\right)^{nt}=A$$

The equation is in standard form.

$$\left(\frac{n+r}{n}\right)^{nt}P=A$$

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

$$\frac{\left(\frac{n+r}{n}\right)^{nt}P}{\left(\frac{n+r}{n}\right)^{nt}}=\frac{A}{\left(\frac{n+r}{n}\right)^{nt}}$$

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

$$P=\frac{A}{\left(\frac{n+r}{n}\right)^{nt}}$$

Solve for A (complex solution)

$$A=P\times \left(\frac{n+r}{n}\right)^{nt}$$

$$n\neq 0$$

Solve for A

$$A=P\times \left(\frac{n+r}{n}\right)^{nt}$$

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