Almost everything written about compounding stops at the observation that growth accelerates. That is true and not very useful. What decides your actual outcome is the interaction between three things: the rate, how often interest is applied, and how long the money is left alone. The third one dominates the other two by a wide margin, which is why a modest rate held for thirty years beats an impressive rate held for eight.
Compounding frequency is the part most often oversold. Moving from annual to monthly compounding at the same nominal rate does change your return, but the effect is small enough that it is usually swamped by a difference of a fraction of a percent in the rate itself. The guides here quantify that rather than asserting it, so you can tell when frequency is worth chasing and when it is a distraction from the number that matters. If you want to see the size of the effect on your own figures, the compound interest calculator lets you hold everything else fixed and change only the compounding periods.
Shortcuts get their own treatment. The Rule of 72 is a good mental estimate and a poor basis for a plan, because it assumes a single lump sum growing at a fixed rate with nothing added and nothing withdrawn. The moment you contribute monthly, or take money out, or the rate varies, the rule stops describing your situation. Knowing exactly where an approximation stops being safe is more valuable than knowing the approximation.
Read these in roughly the order of mechanism first, then frequency, then the estimation shortcuts. If you already understand the formula, skip to the frequency comparisons, since that is where most of the practical disagreements live.
