Compound interest explained, with the maths made simple

Simple interest versus compound interest

Simple interest is calculated only on your original amount, so if you put £1,000 into an account paying 5% simple interest, you earn £50 every year, forever, on that same original £1,000. The interest never earns interest of its own.

Compound interest is different: once interest is added to your balance, it becomes part of the amount that earns interest the following period. So after year one you have £1,050, and in year two you earn 5% on £1,050 rather than on the original £1,000, giving you £52.50 rather than £50.

The gap between simple and compound interest looks tiny in year one but widens every year after that, because each year's interest is calculated on a slightly larger base than the year before.

Why time matters more than most people expect

Because compounding builds on itself, the biggest gains typically show up in the later years of a long savings period, not the early ones. Someone saving steadily for 30 years will often see more growth in the final decade than in the first two decades combined, purely from compounding on an accumulated balance.

This is also why starting early carries such an advantage. Someone who saves for 10 years in their twenties and then stops can end up with more at retirement than someone who saves twice as much per month but only starts in their forties, purely because the first saver's money had longer to compound.

None of this is guaranteed, since real returns depend on the actual rate achieved and can go down as well as up for investments, but the mathematical principle of compounding itself is straightforward and reliable for a fixed rate.

The rule of 72, a quick mental shortcut

A well-known shortcut for estimating how long money takes to double is to divide 72 by the annual interest rate. At 6% a year, money roughly doubles in 72 divided by 6, which is 12 years; at 4% it takes roughly 18 years.

This is an approximation rather than an exact calculation, and it becomes less accurate at very high or very low rates, but it is a handy way to sanity-check a savings calculator's output or to compare two different rates quickly in your head.

It also illustrates why even a modest difference in rate matters over long periods: the difference between doubling in 12 years versus 18 years compounds into a substantial gap by the time you reach retirement age.

How compounding frequency changes the outcome

Interest can compound annually, monthly, daily, or at other intervals, and more frequent compounding produces a slightly higher effective return for the same headline annual rate, because interest starts earning its own interest sooner. The difference between annual and monthly compounding is usually small but not zero.

This is why savings products sometimes quote both an annual equivalent rate, or AER, which standardises for compounding frequency, and a gross rate, which does not. Comparing AER figures across products gives you a fairer like-for-like comparison than comparing gross rates.

For most everyday savings decisions the compounding frequency matters far less than the headline rate and how long you leave the money invested, but it is worth checking the AER when comparing very similar-looking products.

A worked example over 20 years

Take £5,000 saved today, plus £100 added every month, growing at an estimated 5% a year, compounded annually for simplicity. In the first few years the balance grows mostly from your own contributions, since the interest earned on a relatively small balance is modest in absolute terms.

By year 20, the picture looks quite different: a meaningful share of the total balance comes from accumulated interest rather than contributions, because interest has been compounding on an increasingly large base for two decades. The exact split depends on the real rate achieved, which is never guaranteed.

Plugging numbers like these into a savings calculator lets you see the year-by-year build-up rather than just the final figure, which makes the effect of compounding far more tangible than a single end number.

Compound interest working against you: debt

The same maths that grows savings also grows debt if interest is left unpaid, which is why credit card balances can spiral if only minimum payments are made. Interest is added to the balance, and next month's interest is calculated on that larger balance, compounding against you rather than for you.

This is one of the clearest reasons to prioritise clearing high-interest debt before focusing heavily on savings, since the compounding effect on an 20%+ credit card rate works far faster against you than most savings rates work in your favour.

Understanding compounding in both directions, growing your savings and shrinking your debt, gives a clearer sense of where extra money is best directed at any given time.

Inflation and the real value of compounding

A return that looks impressive in cash terms can be less impressive once inflation is accounted for, since prices rising over the same period erode the purchasing power of your growing balance. A savings account paying 4% when inflation is running at 3% is only growing your real spending power by roughly 1% a year.

This does not mean compounding is not worthwhile, but it is worth thinking in terms of real, inflation-adjusted growth rather than headline nominal figures when planning for a long-term goal like retirement or a house deposit many years away.

Tax can have a similar eroding effect outside tax-free wrappers like ISAs, so where you hold long-term savings matters almost as much as the rate you earn on them.

Common questions

What is the difference between AER and gross interest rate?

Gross rate is the interest rate before accounting for how often interest compounds, while AER, or annual equivalent rate, standardises for compounding frequency so you can fairly compare products that pay interest monthly against those that pay annually. Always compare AER figures when choosing between similar savings accounts.

Does compound interest apply to all savings accounts?

Most UK savings accounts compound interest, though the frequency varies, some daily, some monthly, some annually, and this is usually stated in the account terms or shown via the AER. Fixed-rate bonds and some current accounts may pay interest differently, so check the specific product details.

How much difference does starting five years earlier really make?

It can be substantial, because those extra five years of compounding happen at the point in your timeline when the growing balance benefits most from further growth. The exact difference depends on the rate achieved and how much you contribute, but starting earlier consistently outperforms starting later with the same total contributions, all else equal.

Can compound interest work against me?

Yes, on debt such as credit cards or overdrafts, unpaid interest is added to your balance and then itself accrues further interest, which is why unpaid high-interest debt can grow quickly. This is a strong reason to prioritise clearing expensive debt before focusing purely on growing savings.

Is the rule of 72 accurate?

It is a useful approximation for typical savings and investment rates, generally within a reasonable margin of the exact answer, but it becomes less precise at very high or very low interest rates. For a precise figure, a savings calculator will give you an exact year-by-year projection rather than an estimate.

Tools for this

• Savings Interest Calculator