How does compound interest work, on savings and on debt?

Compound interest is not a financial product and there is nothing to buy. It is a description of what happens when interest is added to a balance rather than paid away. Understanding it changes two decisions: how early you start saving, and how urgently you clear expensive debt.

Step by step

1. See the difference from simple interest.Simple interest is calculated on the original amount each period. Compound interest is calculated on the balance including interest already added, so each period starts from a larger number.
2. Notice that the effect is slow then fast.For the first few years compounding looks disappointing. The curve steepens later, which is exactly why people give up on it before it does anything.
3. Compare on AER, not the headline rate.AER on savings expresses the rate with compounding included, so it is the figure that lets you compare accounts paying interest monthly against ones paying annually.
4. Compare borrowing on APR.APR is the equivalent for credit, including compounding and mandatory fees. It exists so different products can be compared on one number.
5. Check how often interest is added.Monthly compounding at the same nominal rate produces slightly more than annual compounding. AER accounts for it, which is why AER is the comparison figure.
6. Apply it to debt.Credit card interest is typically charged monthly on the outstanding balance including previous interest. A minimum payment barely covers it, which is why balances persist for years.
7. Understand why clearing expensive debt beats saving.Paying off debt at a high rate is a guaranteed return equal to that rate. It is very difficult to beat that with savings, which is why most guidance says clear expensive debt first.
8. Remember inflation works on the same principle.Prices compound too, so money held at a rate below inflation loses purchasing power steadily even as the number grows.
9. Use a calculator rather than a rule of thumb.MoneyHelper has free compound interest and debt repayment calculators. Seeing your own numbers is far more persuasive than any general example.

Tips

• Time is the ingredient you cannot buy later. A smaller amount started earlier frequently beats a larger amount started later.
• Paying more than the minimum on a card is the single highest-return use of spare money for most households with card debt.
• AER for savings and APR for borrowing exist so you can compare like with like. Use them and ignore the marketing rate.

Common mistakes

• Giving up in the flat part of the curve — Compounding does very little visibly in the early years and most of its work later. Stopping early removes exactly the part that mattered.
• Saving while carrying expensive debt — The debt usually compounds faster than the savings, so the household goes backwards while feeling responsible. Keep a small emergency buffer, then attack the debt.

If it doesn't work

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