How compound interest works, the formula with worked UK examples, the effect of compounding frequency, the rule of 72, inflation, fees, and how compounding works against you on debt.
Compound interest means earning interest on your interest. Over long periods, it is one of the most powerful forces in personal finance: it helps savings and investments grow, and makes unpaid debts grow too. Understanding the formula helps you compare accounts, see the cost of fees and decide whether to save or pay off debt.
Simple vs compound interest
- Simple interest is calculated only on the original amount. £1,000 at 5% simple interest earns £50 a year, every year.
- Compound interest is calculated on the original amount plus interest already added. £1,000 at 5% compounded annually becomes £1,050 after one year, then £1,102.50 after two, because the second year's interest is calculated on £1,050.
The formula
A = P × (1 + r/n)n×t
- A = final amount
- P = starting amount (principal)
- r = annual interest rate as a decimal (5% = 0.05)
- n = number of times interest is compounded per year
- t = number of years
Worked examples
A lump sum
£10,000 at 4% compounded annually for 10 years: £10,000 × 1.0410 ≈ £14,802. Simple interest would give £14,000, so compounding added about £802.
Over 30 years
The same £10,000 at 4% for 30 years grows to about £32,434. With simple interest it would be £22,000. The longer the time, the bigger the difference.
Regular saving
Saving £200 a month at 4% a year, compounded monthly, for 20 years gives about £73,000, of which £48,000 is your contributions and around £25,000 is interest. Online savings calculators handle regular payments easily.
Compounding frequency
Interest added more often grows slightly faster. £10,000 at 5% for one year gives £10,500 compounded annually, but about £10,512 compounded monthly. This is why UK savings accounts quote the AER (annual equivalent rate), which shows the effect of compounding over a year, making accounts comparable.
The rule of 72
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, about 12 years; at 3%, about 24 years. It's an approximation, but useful for quick comparisons.
Inflation: the real return
If savings earn 4% but prices rise by 3%, your real return is roughly 1%. Over long periods, inflation can erode savings held in low-interest accounts. Investments have historically beaten inflation over long periods, but values can fall and returns aren't guaranteed.
Fees compound too
Investment and pension fees reduce your return every year, so they compound against you. On £10,000 growing at 5% for 30 years, a 1% annual fee rather than 0.25% could reduce the final value by many thousands of pounds. Always check the total ongoing charges.
Compounding on debt
Debt compounds too. Credit card interest is usually charged monthly on the outstanding balance. A £3,000 balance at around 25% APR, paying only a small minimum each month, can take many years to clear and cost thousands in interest. That's why paying off expensive debt usually beats saving.
How do you make compounding work for you?
- Start early: time matters more than the amount.
- Save regularly, ideally automatically on payday.
- Reinvest interest and dividends rather than withdrawing them.
- Use tax-free wrappers such as ISAs and pensions, so tax doesn't reduce growth.
- Keep fees low.
- Pay off high-interest debt first.
Frequently asked questions
Does compound interest apply to ISAs?
Yes. Interest in a cash ISA compounds like any savings account, and growth isn't taxed.
Is AER the same as APR?
No. AER is for savings, showing interest earned. APR is for borrowing, including interest and some fees.
Do fixed-rate savings compound?
Depends on the account. Some pay interest annually or at maturity; others pay monthly. Check whether interest is added to the balance or paid out.
Sources and further reading
Facts checked on 20 October 2026. Spotted an error? Tell us and we will correct it.