So far money has walked forwards in time, growing as it goes. Present value walks it backwards: if someone promises you $\mathit{FV}$ dollars in $t$ years, what is that promise worth today? Undo the growth — divide by the factor instead of multiplying: $\mathit{PV} = \dfrac{\mathit{FV}}{(1 + r)^{t}}$ — read aloud: PV equals FV over one-plus-r to the t.

The idea underneath is worth keeping for life: a dollar promised for next year is worth LESS than a dollar in your hand, because the dollar in hand could be growing already. Dividing by $(1 + r)^{t}$ is exactly compound interest run in reverse — same factor, opposite direction. And a free answer check: if your value-today comes out BIGGER than the promise, you multiplied when you should have divided.