Answer
$i = \pm 100\sqrt {\frac{A}{P}} - 100$
Work Step by Step
$Solve$ $the$ $equation$ $for$ $the$ $indicated$ $variable:$
$A = P(1+\frac{i}{100})^2;$ $for$ $i$
Solve for $i$
Divide both sides by $P$
$\frac{A}{P} = \frac{P(1+\frac{i}{100})^2}{P}$
$\frac{A}{P} = (1+\frac{i}{100})^2$
Square root both sides
$\pm \sqrt {\frac{A}{P}} = \sqrt {(1+\frac{i}{100})^2}$
$\pm \sqrt {\frac{A}{P}} = 1+\frac{i}{100}$
Subtract 1 from both sides
$\pm \sqrt {\frac{A}{P}} - 1 = 1+\frac{i}{100} -1$
$\pm \sqrt {\frac{A}{P}} - 1 = \frac{i}{100}$
Multiply both sides by 100
$100(\pm \sqrt {\frac{A}{P}} - 1) = 100(\frac{i}{100})$
$i = \pm 100\sqrt {\frac{A}{P}} - 100$
