Solve for r a=p(1+rt)

$a = p (1 + r t)$

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.

$r = \frac{a}{p t} - \frac{1}{t}$