Compound interest explained with UK savings examples

Compound interest is interest earned on the interest you have already received, as well as on the money you put in. Over a few months the effect is tiny, but over decades it becomes the main reason a steady saver ends up with much more than they put in. It works the other way on debt, where it is why balances grow so fast. This guide explains the idea in plain terms, gives the formula, works through examples for a lump sum and for monthly saving, shows the rule of 72 for quick estimates, and covers the points that change the real-world result: how often interest is added, inflation, and the tax treatment of savings in the UK in the 2026/27 tax year.

By Valtrinity. Updated 18 October 2026.

Simple and compound interest

With simple interest, you earn interest only on the original sum. £5,000 at 5 per cent simple interest earns £250 a year, every year, so after 10 years you have earned £2,500.

With compound interest, each year's interest is added to the balance, and the next year's interest is calculated on the larger total. After one year £5,000 at 5 per cent becomes £5,250. In the second year, interest is 5 per cent of £5,250, which is £262.50, giving £5,512.50. After 10 years the balance is £8,144.47, so the interest earned is £3,144.47, which is about £644 more than with simple interest.

The longer the money stays in, the bigger the gap. This is why starting early matters more than most people expect.

The formula

For a lump sum, the amount after n years is the starting amount times (1 plus the annual rate) raised to the power n. In symbols: A = P × (1 + r)^n, where r is the rate as a decimal. If interest is added more often than yearly, use A = P × (1 + r ÷ m)^(m × n), where m is the number of times a year interest is added.

Example: £1,000 at 5 per cent for 10 years with interest added once a year is 1,000 times 1.05 to the power 10, which is £1,628.89. If interest is added monthly at a nominal 5 per cent a year, the monthly rate is 0.05 divided by 12, and the balance after 120 months is £1,647.01. The more frequent adding gives £18.12 more.

For comparing accounts, use the AER, the annual equivalent rate, which already allows for how often interest is added. Two accounts with the same AER give the same result over a year, whatever the schedule.

The effect of time and rate

Take £1,000 left alone at different rates. At 2 per cent for 10 years it becomes £1,219. At 5 per cent for 30 years it becomes £4,322. At 7 per cent for 30 years it becomes £7,612. Notice how two extra percentage points nearly double the result over a long period.

Time does even more. £1,000 at 5 per cent grows to £1,629 after 10 years, £2,653 after 20 years and £4,322 after 30 years. Each decade adds more than the one before it, because the base is bigger.

Rates of return in the real world rise and fall. A fixed-rate savings bond pays a known rate for a fixed term. Investments in shares can grow faster over long periods, but the value can fall as well as rise, and you may get back less than you put in. Compound interest as shown here is a calculation, not a forecast.

Saving a regular amount each month

Most people save a little each month rather than a single lump sum. Suppose you put away £200 a month for 20 years. That is £48,000 of your own money.

At a rate of 5 per cent a year, added monthly, the pot grows to about £82,207. The extra £34,207 is interest. At 4 per cent, the pot is about £73,355. At 3 per cent, it would be about £65,660, which shows how sensitive long-term saving is to the rate.

If you start 10 years later and want to reach the same pot of £82,207 in 10 years at 5 per cent, you need to save much more each month, about £529. Starting early lets time do the heavy lifting, while starting late means your own contributions have to do more of the work.

The rule of 72

A quick way to estimate how long it takes money to double is to divide 72 by the annual percentage rate. At 6 per cent, 72 divided by 6 is 12, so money doubles in about 12 years. The exact figure is 11.9 years. At 4 per cent it is 18 years, with the exact answer 17.7.

The rule works well for rates between about 4 and 12 per cent. It also works for inflation and for debts. If prices rise by 3 per cent a year, 72 divided by 3 is 24, so prices double in about 24 years, and the buying power of cash halves in the same time.

It is only an estimate, but it is easy to do in your head and good for sense-checking a figure from a calculator.

Inflation: the real return

A rate of interest means little without inflation. If your savings earn 4 per cent and prices rise by 3 per cent, your real return is only about 1 per cent. If prices rise faster than your interest, your money buys less than before even though the balance is larger.

A quick illustration: £10,000 with prices rising at 3 per cent a year buys only what £7,441 buys today after 10 years. To keep up, the savings would have to grow to £13,439 in the same period. Over a long time, inflation matters as much as the interest rate.

This is why savers look at the rate after inflation and why they sometimes consider other types of saving and investment for long-term goals. For money you need within a few years, an easy-access or fixed-rate account is usually the more appropriate home.

Tax on savings in 2026/27

In the 2026/27 tax year, you can put up to £20,000 into ISAs, and the interest or gains inside an ISA are not subject to UK tax. The rules about the types of ISA and any limits on how much can go into cash may change, so check GOV.UK for the latest position.

Outside an ISA, savings interest is taxable, but most people pay none because of two allowances. The starting rate for savings lets some people with low other income receive up to £5,000 of interest at 0 per cent. The Personal Savings Allowance is £1,000 a year for basic-rate taxpayers, £500 for higher-rate taxpayers and nothing for additional-rate taxpayers.

For example, at 5 per cent, a basic-rate taxpayer reaches the £1,000 allowance with £20,000 of savings. A higher-rate taxpayer reaches the £500 allowance with £10,000. Above that, interest is taxed at your usual rates.

Tools mentioned in this guide

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