Leave the interest IN the account and it starts earning interest of its own: $A = P\,(1 + i)^{n}$ — read aloud: A equals P, times one-plus-i to the n. Each period multiplies the whole balance by $1 + i$, and $n$ periods stack as a power — this is the geometric sequence with $r = 1 + i$, wearing a bank uniform. Compounded monthly? Same formula, smaller gears: $i$ becomes the yearly rate ÷ 12, and $n$ counts MONTHS, twelve per year.

Read backwards, the same machine prices the future: $\mathit{PV} = \mathit{FV}/(1 + i)^{n}$ — what a promised amount is worth today. Growing multiplies; discounting divides; there is one formula here, not two. The gap between simple and compound looks like pocket change at year two and is a canyon by year twenty — compounding is patient money's superpower.