Compound Interest Explained: The Maths, the Rule of 72 & ISA Examples (UK 2026/27)

Quick answer

Compound interest is simply earning a return on your returns. In year one you earn interest on your deposit; in year two you earn interest on the deposit plus last year's interest; and so on. Because the base keeps growing, the gains accelerate — slowly at first, then dramatically. The two things that supercharge it are time and keeping the taxman out, which is why a £20,000-a-year ISA is a UK saver's best friend. This guide covers the maths, the famous Rule of 72, and worked tax-free examples for 2026/27.

Simple vs compound interest

Simple interest is calculated only on your original sum. Put £10,000 in at 5% simple interest and you earn £500 every year — £5,000 over a decade, ending at £15,000.

Compound interest adds each year's interest to the balance, so the next year's interest is calculated on the larger amount. The same £10,000 at 5% compound grows like this:

• Year 1: £10,000 × 1.05 = £10,500
• Year 2: £10,500 × 1.05 = £11,025
• Year 3: £11,025 × 1.05 = £11,576
• …
• Year 10: £16,289

That extra £1,289 over simple interest is the compounding effect — and over 30 years the same £10,000 reaches £43,219, more than four times your money, without adding a penny. Try it with the

.

The formula

The standard compound interest formula is:

A = P × (1 + r/n)^(n×t)

Where:

• A = final amount
• P = principal (your starting sum)
• r = annual interest rate (as a decimal, so 5% = 0.05)
• n = number of times interest compounds per year (1 for annual, 12 for monthly)
• t = number of years

The key insight is the exponent: the longer the time (t) and the more frequent the compounding (n), the larger the result. More frequent compounding helps a little — monthly compounding at 5% gives an effective annual rate of about 5.12% — but it is the t in the exponent that does the real work over decades.

The Rule of 72: doubling made easy

You rarely need the full formula to grasp the power of compounding. The Rule of 72 estimates how many years it takes to double your money: divide 72 by the annual percentage return.

• At 3%: 72 ÷ 3 = 24 years to double
• At 6%: 72 ÷ 6 = 12 years
• At 8%: 72 ÷ 8 = 9 years
• At 10%: 72 ÷ 10 = 7.2 years

So a portfolio returning a long-run average of 7% doubles roughly every decade. Over a 40-year working life that's around four doublings — meaning £10,000 invested at 25 could become roughly £160,000 by 65, before adding any further contributions. The Rule of 72 also works in reverse for inflation: at 3% inflation, prices double — and your cash loses half its purchasing power — in 24 years.

Why time beats money

The most counter-intuitive lesson is that when you start matters more than how much you start with. Compare two savers, both targeting age 65 at a 6% average return:

• Maya invests £200/month from age 25. Over 40 years she contributes £96,000 and ends with roughly £398,000.
• Tom invests £400/month from age 45. Over 20 years he contributes the same £96,000 but ends with only about £185,000.

Identical total contributions, but Maya's pot is more than double Tom's — purely because her early money had twice as long to compound. The first decade of saving, when the balance looks trivially small, is doing the most important work. This is the single strongest argument for starting young, even with modest amounts. See the effect for your own dates with the

.

The ISA advantage: compounding tax-free

Compounding is fastest when nothing is skimmed off along the way — and that is exactly what an ISA delivers. For 2026/27 you can pay in up to £20,000 across your ISAs, and all interest, dividends and capital gains inside are completely tax-free, with nothing to declare on a tax return.

Outside an ISA, tax nibbles the base that compounds. A higher-rate taxpayer earning 5% on savings beyond their £500 Personal Savings Allowance loses 40% of the interest above it, dropping the effective rate to 3%. Over 30 years, that difference between 5% and 3% on £20,000 is the gap between roughly £86,000 and £49,000 — the taxman quietly costs you tens of thousands. The

shows the tax-free trajectory.

Worked ISA example

Priya pays the full £20,000 into a stocks and shares ISA each April and earns a long-run 6% average:

• After 10 years: ~£279,000 (contributions £200,000)
• After 20 years: ~£779,000
• After 25 years: ~£1.16m

Every penny of that growth is tax-free and need never appear on a Self Assessment return. Even at a more modest £500/month, the same 6% over 25 years builds toward £345,000 — entirely sheltered. Reinvesting dividends rather than spending them is what keeps the snowball rolling.

Compounding against you: debt

The same maths that builds wealth destroys it on the other side of the ledger. Credit cards, store cards and overdrafts compound interest on your balance — unpaid interest itself starts earning interest. At a typical 25% credit card APR, the Rule of 72 says the debt could double in under three years if you only pay the minimum.

This is why financial planners almost universally say: clear high-interest debt before investing. Paying off a 25% card is a guaranteed, tax-free 25% return — far better than any realistic investment. Model your payoff with the

before deciding where spare cash should go.

How inflation erodes the gains

A final reality check: compound growth competes with compound inflation. If your money grows 5% but prices rise 3%, your real return is only about 2%. Cash savings paying less than inflation are losing purchasing power even as the balance number rises. This is the core argument for investing for long-term goals rather than holding everything in cash — over decades, the equity premium has historically outpaced inflation by a wide margin, whereas cash rarely keeps up. The

shows how purchasing power changes over time.

Regular contributions: compounding a habit

The examples so far mostly grow a single lump sum, but most people build wealth by adding regularly. When you contribute every month, each instalment starts its own compounding journey — the money you pay in at 25 compounds for 40 years, while the money you pay in at 60 compounds for only a few. This is why a steady monthly habit is so powerful: you're constantly planting new seeds, and the early ones grow into the largest trees.

The maths of a regular contribution is the "future value of an annuity," but the intuition is simpler than the formula. Pay £300 a month for 30 years at 6% and you contribute £108,000 — yet you end with roughly £295,000. Nearly two-thirds of the final figure is growth, not your own money. Pound-cost averaging is a useful side effect: by investing the same amount each month you automatically buy more units when prices are low and fewer when high, smoothing out the bumps and removing the temptation to time the market. The

lets you model a monthly contribution alongside a starting lump sum.

Frequency of compounding: does it matter?

People often fixate on whether interest compounds daily, monthly or annually. It matters less than you'd think. At a 5% nominal rate:

• Annual compounding gives an effective rate of exactly 5%.
• Monthly compounding gives about 5.12%.
• Daily compounding gives about 5.13%.

The jump from annual to monthly is small, and from monthly to daily it's negligible. This is why the Annual Equivalent Rate (AER) exists — it standardises savings accounts to a single comparable figure that already accounts for compounding frequency, so you can compare a daily-compounding account against an annual one fairly. When choosing a savings account, compare the AER, not the headline rate, and don't lose sleep over compounding frequency — the rate itself and the time invested dominate.

Where compound interest shows up in your life

It's worth recognising compounding wherever it appears, because the same engine drives very different outcomes:

• Pensions: decades of tax-relieved, employer-matched, tax-free growth — the single most powerful compounding vehicle most people will ever use. See our pension tax relief guide for why.
• ISAs: tax-free compounding you can access before retirement, with the £20,000 annual allowance.
• Reinvested dividends: a huge share of long-run stock-market returns comes from reinvesting dividends rather than spending them — switching them off cripples the snowball.
• Mortgages: overpaying early saves compounding interest you'd otherwise pay the lender; £100 overpaid in year one of a 25-year mortgage saves far more interest than £100 overpaid in year 20.
• Inflation: the silent compounding that erodes idle cash.

Recognising which side of the ledger you're on — earning compound returns or paying compound costs — is the core skill. The

shows the most dramatic version of the upside.

The cost of waiting "just a few years"

A final way to feel the power of time: every year you delay starting doesn't just cost you that year's contribution — it costs you that contribution's entire future compounded value. Delay starting a £250-a-month pension by five years, from 25 to 30, and at a 6% return you don't lose £15,000 (the five years of contributions); you lose closer to £90,000 of final pot, because those early contributions would have compounded for the longest. "I'll start when I earn more" is the most expensive sentence in personal finance. Even a small amount started now beats a larger amount started later — start with whatever you can, and increase it as your income grows.

Real returns: subtracting inflation and charges

Two quiet forces sit between the headline return and the wealth you actually keep: inflation and charges. Inflation erodes purchasing power, so what matters for your future spending is the real return — roughly the nominal return minus inflation. A 6% return alongside 3% inflation is really about 3% in spending power. Charges work the same way: a fund charging 1% a year, plus a 0.5% platform fee, drags 1.5% off your return every single year — and because of compounding, that small annual leak balloons over decades.

Consider £100,000 over 30 years at a 6% gross return. With no charges it grows to about £574,000; with 1.5% annual charges (net 4.5%) it grows to only about £375,000. That 1.5% fee quietly cost you nearly £200,000 — almost as much as the original investment. This is why low-cost index funds inside a tax-free ISA are so often recommended: they let the maximum amount of return compound for you rather than for the fund manager and the taxman. When comparing investments, always think in terms of net real returns, not headline rates. The

shows how purchasing power changes over the same horizons.

A mental model you can carry around

If you remember nothing else, carry three numbers in your head. First, the Rule of 72 for doubling time — it lets you sanity-check any return claim on the spot ("11% a year? That doubles my money in under seven years — is that realistic?"). Second, that time in the market beats the size of your contribution, so starting is more urgent than starting big. Third, that fees and inflation compound against you just as returns compound for you, so a 1% difference in charges is never trivial over a lifetime. With those three ideas you can evaluate almost any savings or investment decision without a calculator — and then use the

to confirm the exact figures before you commit.

Putting it all together

Compound interest is the closest thing personal finance has to a free lunch — but only if you give it time and stop the taxman taking a cut. Understand the formula, use the Rule of 72 as a mental shortcut, start as early as you possibly can even with small sums, and shelter your investments inside your £20,000 ISA allowance so every penny of growth compounds tax-free. And remember the dark mirror: the same force that builds a six-figure ISA will balloon a credit card balance, so clear expensive debt first. Run your own numbers with the

and the .

This article is general information, not financial advice. Figures use 2026/27 UK ISA allowances and illustrative returns; actual investment returns are not guaranteed and can fall as well as rise.