Solve for r A=P(1+rt) for r

$A = P (1 + r t)$ for $r$

Step 1

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

$P (1 + r t) = A$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $P$ .

Cancel the common factor.

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

Divide $1 + r t$ by $1$ .

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

Step 3

Subtract $1$ from both sides of the equation.

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

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $t$ .

Cancel the common factor.

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

Divide $r$ by $1$ .

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

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

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

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

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

Move the negative in front of the fraction.

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