Annuity present value formula explanation

Question

Could somene please explain me how the formula evolves, ie. how does the fraction flip, etc? Thank you in advance!

Answer 1

Is that what you are asking?

\begin{equation} \begin{split} \frac{1 - [1/(1+r)^t]}{r} &= \frac{1 - \frac{1}{(1+r)^t}}{r} \\ &= \frac{1}{r} \bigg( 1- \frac{1}{(1+r)^t}\bigg) \\ &= \frac{1}{r} - \frac{1}{r(1+r)^t} \end{split} \end{equation}