Simple interest vs compound interest: the one misconception that breaks both

Ask most Essential or General Maths students to recite the simple interest formula and the compound interest formula, and they usually can. Ask them to explain why compound interest grows faster, and the room goes quiet.

The misconception isn't the formula

Students rarely mix up I = Prt and A = P(1+r)ⁿ as symbols — they can look them up, or have them on a formula sheet. What trips them up is a conceptual gap underneath both: they think of interest as something that happens to the principal, rather than understanding that compound interest changes what counts as principal over time.

This matters because it's the same misconception that causes errors on multi-step compound interest problems later — students who don't understand that the base amount changes each period will often apply the rate to the original principal every time, effectively turning a compound interest question into a simple interest one by accident.

A way to make it visible

Rather than starting with the formula, it helps to build a small table by hand for 3–4 periods — principal, interest earned, new principal — before ever writing A = P(1+r)ⁿ on the board. Once a student has manually recalculated the "new principal" three times, the formula stops being an abstract rule and starts being a shortcut for something they've already done by hand.

Where this comes from

The Compound Interest resource in the catalogue builds this in deliberately — the worked examples walk through the period-by-period table before introducing the closed-form formula, so the "why" lands before the "how."