What is compound interest? A UK saver's guide with worked examples

With simple interest, you earn the same amount each year because it is only ever calculated on your original deposit. With compound interest, each year's interest is added to the balance and earns interest itself.

The gap is small at first and grows wider every year. That is why time matters so much: compounding does most of its work in the later years.

UK savings accounts quote an AER (annual equivalent rate). AER shows what you would earn over a year if interest were paid and left in the account, taking compounding into account. It lets you compare accounts that pay interest monthly with those that pay annually.

Accounts may also show a gross rate, which is the rate before tax and before the effect of compounding. An account paying interest monthly will have a gross rate slightly lower than its AER. When comparing accounts, use AER. Our savings rates tool and the hub guide to high-interest savings accounts explain what else to check, such as bonus rates that end after 12 months.

Compounding only works if you leave the interest in the account. If interest is paid out to a different account, you earn simple interest on your balance instead.

Most people save regularly rather than putting in a lump sum. Compounding still applies: each payment starts earning from the day it goes in.

After 30 years, almost half the balance is interest. These examples assume a steady 4% a year, which no account guarantees over decades; rates change and investments go up and down. Try your own figures in the compound interest calculator.

Ten extra years of compounding can make a bigger difference than a larger monthly amount. At 5% a year, £100 a month from age 25 to 65 (£48,000 paid in) grows to about £148,000. Starting at 35 and saving the same until 65 (£36,000 paid in) gives about £82,000. The extra £12,000 paid in by the earlier saver ends up worth around £67,000 more.

This is why workplace pensions and long-term investing benefit so much from an early start, and why even small amounts are worth saving now. The rule of 72 is a quick shortcut: divide 72 by the interest rate to estimate how many years it takes to double your money. At 4%, that is about 18 years.

Tax on interest reduces what is left to compound. Most savers can earn some interest tax-free under the Personal Savings Allowance: £1,000 a year for basic-rate taxpayers, £500 for higher-rate taxpayers and nothing for additional-rate taxpayers. Interest above that is taxed at your income tax rate, and the government has announced that tax rates on savings income will rise by two percentage points from April 2027. Interest earned inside an ISA is tax-free, so it can compound without being reduced by tax. See our guide to the Personal Savings Allowance.

Inflation matters too. If prices rise by 3% a year, £14,802 in ten years' time (what £10,000 becomes at 4%) would buy roughly what £11,000 buys today. Your real growth is the interest rate minus inflation. The inflation calculator shows the effect.

The same maths works against you when you borrow. Credit cards and overdrafts charge interest on unpaid interest, so a balance you do not pay down grows over time. A card with a 24.9% APR quotes a rate that already includes compounding; leave £1,000 untouched for a year and it would grow to about £1,249. Paying off high-interest debt is often the best guaranteed return available, which is why it usually makes sense to clear expensive debt before saving beyond a small emergency fund.

Three habits make the most of compound interest: start as early as you can, save regularly, and leave the interest alone. Choose accounts with a competitive AER, use your ISA allowance if your interest could exceed your Personal Savings Allowance, and think about investing for goals more than five years away. A daily savings habit helps too; SYM tells you how much to put aside each day so the regular payments keep going in.