College Algebra, Chapter 1, 1.1, Section 1.1, Problem 94

Solve the equation $\displaystyle A = P \left( 1 + \frac{i}{100} \right)^2$ for $i$

$\begin{equation} \begin{aligned} A &= P \left( 1 + \frac{i}{100} \right)^2 && \text{Divide both sides by } P\\ \\ \frac{A}{P} &= \frac{\cancel{P}\left( 1 + \frac{i}{100} \right)^2}{\cancel{P}} && \text{Cancel out like terms}\\ \\ \frac{A}{P} &= \left( 1 + \frac{i}{100} \right)^2 && \text{Take the square root of both sides}\\ \\ \pm \sqrt{\frac{A}{P}} &= \sqrt{\left( 1 + \frac{i}{100} \right)^2} && \text{Simplify}\\ \\ \pm \sqrt{\frac{A}{P}} &= 1 + \frac{i}{100} && \text{Subtract both sides by 1}\\ \\ \pm \sqrt{\frac{A}{P}} -1 &= 1 + \frac{i}{100} -1 && \text{Simplify}\\ \\ \pm \sqrt{\frac{A}{P}} -1 &= \frac{i}{100} && \text{Multiply both sides by 100}\\ \\ 100 & \left[ \pm \sqrt{\frac{A}{P}} - 1 = \frac{i}{\cancel{100}} \right] \cancel{100} && \text{Cancel out like terms}\\ \\ 100 \left( \pm \sqrt{\frac{A}{P}} - 1 \right) &= i \\ \\ & \text{or}\\ \\ i &= 100 \left( \pm \sqrt{\frac{A}{P}} -1 \right) \end{aligned} \end{equation}$