Compounding carries money forward. Run the same machine backwards and it carries money back: $\mathit{PV} = \dfrac{\mathit{FV}}{(1 + r)^{t}}$, read aloud as P V equals F V over, one plus r, to the t. $\mathit{FV}$ is the future value — a dollar amount arriving $t$ periods from now. $\mathit{PV}$ is the present value — what that arrival is worth in today's dollars. $r$ is the discount rate per period as a decimal, and $t$ is the number of periods until the money shows up. The one you solve for is whichever end of the bridge the question is standing on.

Why any of this is true: if you had $\mathit{PV}$ today you could invest it and own $\mathit{FV}$ by then. So the two amounts are the SAME money seen from two dates, and $(1+r)^t$ is the exchange rate between them. Every honest comparison of two offers at two dates begins by dragging both to one date — usually today.

Discounting only ever shrinks. If your present value comes out larger than the future amount, you multiplied when you should have divided, and the fix is one keystroke.