Compound Interest Explained (With UK Examples)

Compound interest is the single most important idea in personal finance, and once it clicks, the way you think about saving, investing and borrowing changes for good. In simple terms, it means earning interest on your interest, so your money grows faster and faster over time. The same mechanism that quietly builds wealth in a savings account or pension can also make credit card debt spiral out of control, so it pays to understand both sides.

This guide explains what compound interest really is, shows you the formula in plain terms, and walks through several worked UK examples. No jargon, no sales pitch, just the maths made simple.

What is compound interest?

Interest is the price of money, either what you earn for lending it (savings) or what you pay for borrowing it (loans). With simple interest, you only ever earn or pay interest on the original amount. With compound interest, the interest you earn is added back to the pot, and the next round of interest is calculated on the new, larger balance. Each period, the base grows, so the interest grows too.

Albert Einstein is often (probably wrongly) quoted as calling compound interest the eighth wonder of the world. Apocryphal or not, the sentiment holds: small, steady growth, left alone for long enough, snowballs into something remarkable.

Compound vs simple interest: the key difference

Imagine you save £1,000 at 5% a year. Here is how the two approaches diverge.

With simple interest, you earn £50 every single year (5% of the original £1,000), no matter what. After 10 years you would have £1,000 + (£50 × 10) = £1,500.

With compound interest, year one still earns £50, bringing you to £1,050. But year two earns 5% of £1,050 = £52.50. Year three earns 5% of £1,102.50, and so on. The gap widens every year.

Look at the bottom row. After 30 years, compounding turns your £1,000 into £4,322, while simple interest only reaches £2,500. That extra £1,822 is interest earned on interest, and it cost you nothing but patience.

The compound interest formula

The standard formula looks intimidating but is genuinely straightforward once you name the parts:

A = P (1 + r/n)^nt

• A = the final amount (what you end up with)
• P = the principal (your starting amount)
• r = the annual interest rate, as a decimal (5% = 0.05)
• n = the number of times interest is compounded per year
• t = the number of years

In plain terms: take your interest rate, split it into n chunks across the year, add each chunk to the running total, and repeat for nt total periods. If interest compounds just once a year, n = 1 and the formula simplifies to the familiar A = P(1 + r)^t.

Quick check: £1,000 at 5% compounded yearly for 10 years = 1,000 × (1 + 0.05)¹⁰ = 1,000 × 1.6289 = £1,628.89. That matches the table above.

Why compounding frequency matters

The n in the formula is the compounding frequency. The more often interest is added, the more often you start earning interest on that interest, so the final figure nudges higher. Here is £1,000 at a 5% annual rate over 10 years, compounded at different frequencies:

The difference between annual and daily compounding is real but modest, about £20 here. The headline rate matters far more than the frequency, but it is worth knowing why two accounts quoting the same rate can pay slightly different amounts.

This is what AER is for

Because compounding frequency muddies comparisons, UK savings accounts must quote an AER (Annual Equivalent Rate). AER shows what you would earn over a year if interest were paid and compounded, putting every account on a level playing field. When you compare savings accounts, compare the AER, not the headline monthly rate. For borrowing, the equivalent standardised figure is the APR (Annual Percentage Rate), which also folds in fees.

Prefer to model your own numbers? Use our full Compound Interest Calculator or the Savings Calculator to add regular monthly contributions.

The Rule of 72: mental maths for doubling

You do not always need a calculator. The Rule of 72 is a handy shortcut that tells you roughly how many years it takes for money to double at a given compound rate:

Years to double ≈ 72 ÷ interest rate

• At 6%: 72 ÷ 6 = 12 years to double
• At 4%: 72 ÷ 4 = 18 years to double
• At 9%: 72 ÷ 9 = 8 years to double

It also works in reverse for debt: a 24% APR credit card would, in effect, double what you owe in about three years if you never repaid it. The rule is an approximation, but it is remarkably close for typical rates and a brilliant way to sense-check whether a return or a debt is as innocent as it looks.

Worked example: compounding FOR you (savings & investing)

Say you are 30 and you put £200 a month into a Stocks and Shares ISA, and it grows at an average 6% a year (a rough long-run figure for a diversified investment, not guaranteed). You contribute £2,400 a year for 35 years until you are 65.

• Total you actually pay in: £2,400 × 35 = £84,000
• Estimated value at 65 with 6% compound growth: roughly £276,000

Over £190,000 of that pot is growth, not your own contributions. The reason is time: the early pounds compound for three and a half decades. This is why starting in your twenties beats starting in your forties even if the older saver pays in more each month. Inside an ISA (the £20,000-a-year tax-free wrapper) that growth is also free of UK tax, which lets it compound undisturbed.

Outside a tax wrapper, the interest you earn may be taxable, though the Personal Savings Allowance lets basic-rate taxpayers earn £1,000 of savings interest tax-free each year (£500 for higher-rate taxpayers). New to investing? See our guide on how to start investing as a UK beginner.

Worked example: compounding AGAINST you (debt)

Compounding is ruthless when you are the borrower. Suppose you owe £3,000 on a credit card at a typical 24% APR and you only make the minimum payments.

Because interest is charged on the balance each month and any unpaid interest is added to what you owe, the debt compounds against you. Making only minimum repayments, that £3,000 balance can take well over a decade to clear and cost you more in interest than the original amount borrowed. By the Rule of 72, at 24% the debt would otherwise double in about three years.

The lesson is symmetrical: the same force that makes savings snowball makes high-interest debt snowball faster. Clearing expensive debt is usually the highest guaranteed "return" you can get, because paying off a 24% card is mathematically equivalent to earning 24% risk-free.

Common misconceptions

• "Compound interest only matters for big sums." It is driven by time and rate, not size. £50 a month started early can outgrow a much larger lump sum started late.
• "A higher headline rate always wins." Not if compounding frequency or fees differ. Compare the AER for savings and the APR for borrowing.
• "Compound and simple interest are roughly the same." Over one or two years, almost. Over decades, the difference is enormous, as the £1,822 gap in our first table showed.
• "My investments will compound at exactly 6% every year." Investment returns are volatile and not guaranteed; the long-run average smooths out good and bad years. Cash savings rates also move with the Bank of England base rate.
• "Minimum credit card payments are fine." They are designed to keep you in debt for years while interest compounds. Always pay more than the minimum where you can.

Putting it all together

Compound interest rewards three things above all: a decent rate, frequent compounding, and above all time. To make it work for you, start early, keep contributing, shelter growth from tax in an ISA or pension where you can, and never let high-interest debt compound against you. For more on building your finances, browse our personal finance guides.

FAQs

How does compound interest work in simple terms?

You earn interest on your original money, then that interest is added to your balance, so next time you earn interest on the bigger total. Repeated over many periods, your money grows at an accelerating pace because you are always earning interest on a larger and larger base.

What is the compound interest formula?

It is A = P(1 + r/n)^nt, where A is the final amount, P is your starting principal, r is the annual rate as a decimal, n is how many times a year interest compounds, and t is the number of years. If interest compounds once a year it simplifies to A = P(1 + r)^t.

What is the difference between compound and simple interest?

Simple interest is calculated only on the original amount, so you earn the same fixed sum each period. Compound interest is calculated on the original amount plus all previously added interest, so each period earns more than the last. Over long timeframes compound interest produces dramatically larger results.

What is the Rule of 72?

It is a mental shortcut: divide 72 by the annual compound interest rate to estimate how many years it takes for money to double. For example, at 6% it takes roughly 12 years (72 ÷ 6). It works just as well for estimating how quickly debt doubles.

What does AER mean on a savings account?

AER stands for Annual Equivalent Rate. It shows what you would earn over a full year once compounding is taken into account, allowing you to compare savings accounts fairly regardless of whether they pay interest monthly, quarterly or annually. Always compare accounts by AER.

Sources

• MoneyHelper — How compound interest works
• MoneyHelper — AER and APR explained
• Bank of England — The interest rate (Bank Rate)

This guide is general information, not personal financial advice. For your own circumstances, speak to a qualified adviser.