# How do you solve A = P + Prt for t?

Mar 2, 2017

See the entire solution process below:

#### Explanation:

Step 1) Subtract $\textcolor{red}{P}$ from each side of the equation to isolate the $r$ term while keeping the equation balanced:

$A - \textcolor{red}{P} = - \textcolor{red}{P} + P + P r t$

$A - P = 0 + P r t$

$A - P = P r t$

Now, divide each side of the equation by $\textcolor{red}{P} \textcolor{b l u e}{t}$ to solve for $r$ while keeping the equation balanced:

$\frac{A - P}{\textcolor{red}{P} \textcolor{b l u e}{t}} = \frac{P r t}{\textcolor{red}{P} \textcolor{b l u e}{t}}$

$\frac{A - P}{P t} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{P}}} r \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{t}}}}{\cancel{\textcolor{red}{P}} \cancel{\textcolor{b l u e}{t}}}$

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

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

Or

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

$r = \frac{A}{P t} - \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{P}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{P}}} t}$

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

Mar 2, 2017

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

#### Explanation:

Given:$\text{ } A = P + P r t$

Factor out the $P$

$A = P \left(1 + r t\right)$

Divide both sides by P

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

Subtract 1 from both sides

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

Divide both sides by r

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

Or could write this as:

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