Rate comparisons get dismissed because the numbers look close together. A savings account paying 4.5 per cent instead of 4 per cent is "half a per cent better", which sounds like rounding. Over a long enough period it is not rounding, because interest is applied to interest and the gap compounds along with the balance.
Why the gap grows rather than adding up
Simple interest would make the comparison straightforward: half a per cent more each year, every year, on the original amount. Compound interest applies the rate to the balance including everything earned so far, which means the higher rate starts from a larger base each period, and that advantage feeds itself.
The growth factor over n years is (1 + rate)n. Because the rate sits inside a power, a small change to it has an effect that scales with time rather than staying fixed. Doubling the term more than doubles the gap between two rates.
Two places it shows up
Borrowing
On a long mortgage, a fraction of a percentage point is worth checking carefully, because interest is charged on the outstanding balance for decades. The same logic explains why extra repayments have an outsized effect: money paid off the principal early removes every future interest charge that balance would have generated. The loan payment calculator shows both the instalment and the total interest, which is the figure worth comparing between offers.
Saving and investing
The same mechanism runs in your favour. Fees work exactly like a negative rate, which is why a fund charging 1.5 per cent versus 0.5 per cent is a much bigger decision over thirty years than the one-percentage-point difference suggests. The compound interest calculator lets you run both figures and compare the end balances directly.
The rule of 72, and its limits
Dividing 72 by the interest rate gives a rough number of years for money to double: at 6 per cent, about 12 years. It is a useful mental shortcut for comparing rates quickly, and it is accurate enough in the range of about 5 to 10 per cent.
It drifts at the extremes, so it is worth treating as a sanity check rather than a calculation. For anything that matters, run the actual figures with your own rate, term and contribution amounts.
What to compare
Headline rates are not always comparable. Compounding frequency, fees and the timing of contributions all change the outcome, and two accounts quoting the same nominal rate can produce different balances. Comparing the final amount, rather than the advertised percentage, sidesteps all of that in one step.