Solve A = P(1 + rt) for r

Answer

\boxed{r = \frac{A - P}{Pt}}

Substituting this expression back into the original formula yields $A = P\left(1 + \left(\frac{A - P}{Pt}\right)t\right) = P\left(1 + \frac{A - P}{P}\right) = P + A - P = A$ , which confirms the result is correct.

Problem: Solve the formula $A = P(1 + rt)$ for $r$ .

Steps

Divide both sides by $P$ $\frac{A}{P} = 1 + rt$
Subtract $1$ from both sides $\frac{A}{P} - 1 = rt$
Divide both sides by $t$ $r = \frac{\frac{A}{P} - 1}{t}$
Simplify the complex fraction $r = \frac{A - P}{Pt}$

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