How compound interest works
Compound interest is interest earned on interest. Unlike simple interest, which is calculated only on the original amount, compound interest is calculated on both the principal and the accumulated interest from previous periods. The longer the money is left, the larger each year's growth becomes.
The compound interest formula
Where P is the principal (initial deposit), r is the annual interest rate, n is the number of times interest compounds per year, t is the number of years, and PMT is the regular monthly contribution.
Why compounding frequency matters
The more frequently interest is compounded, the more your money grows. Monthly compounding means interest is calculated and added to your balance 12 times per year, while yearly compounding only does this once. With monthly compounding at 5%, your effective annual rate works out at 5.12% because of compounding.
The power of regular contributions
Even small monthly contributions can make an enormous difference over time. Adding just £100 per month to a £10,000 deposit at 5% AER over 20 years turns your total into over £67,000, of which more than £33,000 is interest. Starting early and contributing consistently is one of the most reliable paths to building wealth.
UK savings and tax considerations
In the UK, basic rate taxpayers can earn up to £1,000 in savings interest tax-free each year through the Personal Savings Allowance. Higher rate taxpayers get £500. Interest earned within an ISA wrapper is entirely tax-free. This calculator shows gross (pre-tax) figures, so factor in your tax position when planning.
Worked examples
Each example below was run through the calculator above with the inputs shown. They show gross interest before any tax, and assume the rate stays fixed for the whole term, which real savings rates rarely do.
£10,000 left for 5 years at 4.5% AER, interest paid monthly
No further deposits. The balance reaches £12,461.82, of which £2,461.82 is interest. Because an AER already includes compounding, monthly or yearly interest gives the same answer. If the 4.5% is a gross rate compounded monthly instead, switch the rate type to gross / nominal and the balance is £12,517.96, because the AER on that account is about 4.59%.
£200 a month from nothing, 20 years at 5% AER
You pay in £48,000 over 240 months. The balance ends at £81,160.90, so £33,160.90 is interest. The year-by-year table shows only £12,276.79 of interest by the end of year 13, so more than half of it arrives in the last seven years. That is why the start date matters more than the monthly amount.
£25,000 in an easy-access account paying 4% AER for one year
Leave the rate type on AER and the interest is £1,000.00, whichever frequency you pick. Entering the same 4% as a gross rate compounded monthly shows £1,018.54, which overstates what the bank will pay (see the first mistake below). £1,000 is exactly the Personal Savings Allowance for a basic rate taxpayer, so this saver would pay no tax on it, while a higher rate taxpayer would pay tax on the half above their £500 allowance.
Rules that change the answer
Tax on savings interest
The results above are gross. Outside an ISA, interest counts as income. Your Personal Savings Allowance is £1,000 at the basic rate, £500 at the higher rate and nothing at the additional rate. If your other taxable income is under £17,570, the starting rate for savings can make up to £5,000 of interest tax-free on top, shrinking by £1 for every £1 of other income above your personal allowance. Banks report interest to HMRC after 5 April and HMRC sends a calculation if tax is due (GOV.UK: Tax on savings interest, checked 30 October 2026).
ISAs
Interest, dividends and gains inside an ISA are tax-free and do not need to go on a tax return. In 2026/27 you can put up to £20,000 into ISAs in total, and up to £4,000 of that into a Lifetime ISA (GOV.UK: Individual Savings Accounts, checked 30 October 2026).
Variable and introductory rates
The calculator holds one rate for the whole term. Easy-access rates move with the market, and many accounts pay a bonus rate for the first year only. For those, run the calculator once per rate period and use the closing balance as the next opening deposit.
Common mistakes
Compounding an AER again. Banks quote AER (annual equivalent rate), which already includes the effect of compounding. Leave the rate type on AER for those. Switch it to gross / nominal only when you have the rate before compounding, sometimes shown as the gross rate, and then the frequency you pick matters.
Treating investment growth as interest. A stocks and shares ISA or pension does not pay a fixed rate. Entering 7% shows what a steady 7% would do, but real returns rise and fall and can be negative in a given year.
Forgetting inflation. £81,160.90 in 20 years will buy less than it would today. Compare the rate you are earning with inflation, or use our inflation calculator to see how prices have moved in the past.
How this calculator works: it splits each year into the number of compounding periods you choose and converts the rate to a rate per period (an AER becomes (1 + AER) to the power 1/periods, minus 1, so a year of it pays exactly the AER; a gross rate is divided by the number of periods). It adds interest on the balance at the end of each period, then adds that period's share of your monthly contributions, so a payment starts earning from the following period. Tax allowances were last checked against GOV.UK on 30 October 2026. Every source is listed on our methodology page.