Compound Interest: The Formula, the Intuition and the Traps

Why balances curve upward instead of rising in a straight line, what compounding frequency really changes (less than you think), and the rule of 72 shortcut worth memorising.

The short answer is that it depends on which definition you are working from, and this guide walks through each one. Everything below explains why, and where that answer stops being true.

Why it works this way

Understanding the mechanism matters more than memorising a result. Once you can see which quantity drives the outcome, you can sanity-check any number a tool hands you — including ours — and spot when an input is wrong before the answer misleads you.

A worked example

Start with round numbers you can check in your head, confirm the tool agrees, then move to your real figures. If the simple case is right, the complex one usually is too.

Common mistakes

Three mistakes account for most wrong answers here: mixing units without converting, applying a rate for the wrong period (annual where monthly was needed, or the reverse), and rounding partway through instead of at the end. Each one is easy to make and easy to avoid once you are watching for it.

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Try it yourself

Work through the example with your own figures in the calculator below. Change one input at a time and watch which direction the result moves — that single habit builds more intuition than reading another explanation.