Solve for n A=P(1+nr)

$A = P (1 + n r)$

Step 1

Rewrite the equation as $P (1 + n r) = A$ .

$P (1 + n r) = A$

Step 2

Divide each term in $P (1 + n r) = A$ by $P$ and simplify.

Divide each term in $P (1 + n r) = A$ by $P$ .

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

Simplify the left side.

Cancel the common factor of $P$ .

Cancel the common factor.

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

Divide $1 + n r$ by $1$ .

$1 + n r = \frac{A}{P}$

Step 3

Subtract $1$ from both sides of the equation.

$n r = \frac{A}{P} - 1$

Step 4

Divide each term in $n r = \frac{A}{P} - 1$ by $r$ and simplify.

Divide each term in $n r = \frac{A}{P} - 1$ by $r$ .

$\frac{n r}{r} = \frac{\frac{A}{P}}{r} + \frac{- 1}{r}$

Simplify the left side.

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{n r}{r} = \frac{\frac{A}{P}}{r} + \frac{- 1}{r}$

Divide $n$ by $1$ .

$n = \frac{\frac{A}{P}}{r} + \frac{- 1}{r}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$n = \frac{A}{P} \cdot \frac{1}{r} + \frac{- 1}{r}$

Multiply $\frac{A}{P}$ by $\frac{1}{r}$ .

$n = \frac{A}{P r} + \frac{- 1}{r}$

Move the negative in front of the fraction.

$n = \frac{A}{P r} - \frac{1}{r}$