£
The Money CalculatorUK Tax & Finance Tools
Tax year 2026/27  ·  Bank of England base rate 3.75%
HomeGuidesHow we calculate

The Maths of Compound Growth: How Your Money Really Grows Over Time

By The Money Calculator Team · Updated 2 June 2026 · 10 min read
The short version: compound growth means earning returns on your past returns, so money grows exponentially rather than in a straight line. A lump sum follows future value = principal × (1 + r)^n; regular saving uses the annuity formula. Over decades the growth dwarfs what you put in — but inflation and fees quietly eat into it. The investment calculator does the full sum for you.
You pay in
£100k
It grows to
£250,800
Pure growth
£150,800

Compounding is often called the most powerful force in finance, but the phrase hides simple, knowable maths. Once you can see the formulas, you can see exactly why time matters more than almost anything else, and why small fees do so much damage.

The lump-sum formula

If you invest a single amount and leave it, each period it grows by the return rate, and the next period grows on the new, larger balance. That gives the classic compound formula:

Future value of a lump sumFV = P × (1 + r)^n P = the amount invested r = the return per period (e.g. 0.06 for 6% a year) n = the number of periods

The exponent is what makes it explosive. £10,000 at 6% for 25 years is not £10,000 + 25 lots of interest; it is:

Worked exampleFV = 10,000 × (1.06)^25 = 10,000 × 4.292 = £42,919

The money more than quadruples, even though you never added to it. More than two-thirds of the final figure is growth on growth.

Adding monthly contributions

Most people do not invest once; they drip money in. Each contribution then compounds for a different length of time — the first for the full term, the last for almost none. Summing them gives the future value of an annuity:

Future value of regular contributionsFV = PMT × [ (1 + i)^m − 1 ] ÷ i PMT = the contribution each period i = the return per period (monthly = annual ÷ 12) m = the number of contributions

Take £300 a month for 25 years (300 contributions) at 6% a year, so i = 0.005 a month:

Worked exampleFV = 300 × [ (1.005)^300 − 1 ] ÷ 0.005 = 300 × [ 4.465 − 1 ] ÷ 0.005 = 300 × 693.0 = £207,900

Putting it together

Combine the £10,000 lump sum with £300 a month for 25 years at 6%:

Growth on the £10,000 lump sum£42,919
Growth on the monthly contributions£207,900
Total pot after 25 years£250,800
Total you actually paid in£100,000
Pure growth£150,800

You contributed £100,000 and the market did the other £150,800. That is the whole case for starting early: the growth, not the contributions, becomes the larger part.

Growth What you paid in £260k£130k£0 £250,800 paid in £100k 0510152025 Years

£10,000 up front plus £300 a month at 6% a year. Your contributions (lower band) rise in a straight line, but growth on growth (upper band) curves upward and eventually overtakes everything you paid in. Illustrative.

You put in £100,000; the market added £150,800. Given enough time, the growth — not your contributions — becomes the bigger half.

The rule of 72

For a quick mental estimate of doubling time, divide 72 by the percentage return:

Rule of 72years to double ≈ 72 ÷ annual return (%) at 6%: 72 ÷ 6 = 12 years at 8%: 72 ÷ 8 = 9 years

It is an approximation, but a remarkably good one for the returns most portfolios target, and it makes the cost of waiting vivid: delay ten years and you lose close to a full doubling.

Inflation: growth in real terms

A pot of £250,800 in 25 years will not buy what £250,800 buys today. To see growth in real spending power, deflate by inflation:

Real return and real valuereal return ≈ (1 + nominal) ÷ (1 + inflation) − 1 at 6% nominal and 2.5% inflation: real return ≈ 1.06 ÷ 1.025 − 1 = 3.4% £250,800 ÷ (1.025)^25 ≈ £135,300 in today's money

Still a strong result — but framing it in today's money is more honest, and it is why long-term plans should lean on real, not headline, returns.

Fees: the quiet compounding cost

A platform or fund fee is charged every year on your whole balance, so it compounds against you exactly as growth compounds for you. Run the same £10,000-plus-£300-a-month plan with a 1% annual fee, so the net return is 5% rather than 6%:

Pot at 6% (no fee)£250,800
Pot at 5% (after a 1% fee)£212,500
Cost of a 1% fee over 25 yearsabout £38,300

One percentage point sounds trivial; over 25 years it quietly removes more than a third of your contributions in lost growth. This is why low-cost index funds matter so much over long horizons.

Why time beats timing

Because growth is exponential, the years at the end do the heavy lifting — the pot is largest then, so the same percentage return adds the most pounds. That is the mathematical reason an extra few years invested early outweighs a larger contribution later, and why "time in the market" tends to beat trying to "time the market".

The bottom line

Compound growth is just FV = P × (1 + r)^n applied to a lump sum and, via the annuity formula, to your regular saving. The levers that matter most are time, the return rate, and the fee you pay — and inflation quietly works against all of it. Put your own figures in and watch the curve build.

Project your own lump sum and monthly contributions
Try the investment calculator →

Common questions

What is the formula for compound growth?
For a single lump sum it is future value = principal × (1 + r) to the power of n, where r is the return per period and n is the number of periods. Regular contributions use the future value of an annuity formula, which adds up the growth of each instalment.
What is the rule of 72?
A shortcut for doubling time: divide 72 by your annual percentage return to estimate the years it takes your money to double. At a 6% annual return, money doubles in roughly 12 years.
Should I use real or nominal returns?
Nominal returns ignore inflation; real returns subtract it and show growth in todays spending power. For long-term planning the real return is more meaningful, because a large future sum buys less than the same amount today.
How much difference does a 1% fee make?
Far more than it appears. Because the fee is charged every year on the whole pot, it compounds against you. Over 25 years a 1% annual charge can easily cost tens of thousands of pounds on a moderate portfolio.
Do monthly and annual compounding give different results?
Slightly. More frequent compounding gives a marginally higher result for the same headline rate, because returns are reinvested sooner. The difference is small but grows over long periods.

Sources

MoneyHelper on how compounding works; the figures here are standard compound-interest mathematics. See our full methodology and rates.

MC
The Money Calculator Team
Research & Editorial
Written and reviewed by our editorial team · fact-checked against current HMRC and GOV.UK guidance

These guides are written and maintained by the team behind The Money Calculator — the same people who build the calculators on this site. We aim to explain UK tax and personal finance in plain English and check every figure against current HMRC and government guidance before publishing. This is general information to help you weigh your options, not personal financial advice.

How we calculate Disclaimer

This article is general information for the 2026/27 tax year and not personalised financial advice. Check your own loan details in your student loan account and verify figures against GOV.UK before making decisions.

← All guides