It is not magic. It is a curve that stays flat for a long time and then stops — and every practical lesson follows from its shape.
Compound interest gets described as magic often enough that people stop looking at what it actually does. It is not magic. It is a curve that stays boring for a long time and then stops being boring — and almost every practical lesson about investing follows from the shape of that curve.
Simple interest pays you on your original money. Compound interest pays you on your original money and on all the interest you have already earned.
Year one, the difference is nothing. Year twenty, the difference is most of your balance.
Look at where the shaded area gets thick. For the first decade the two lines barely separate — the money you paid in is doing almost all the work. It is only in the final third that growth pulls decisively away.
That shape is why the most common regret in investing is not a bad fund choice. It is starting late.
The formula for a lump sum is:
Final = Starting amount × (1 + r)^n
where r is the annual growth rate and n is the number of years. £10,000 at 7% for 30 years gives £10,000 × 1.07³⁰ = about £76,100.
For monthly contributions the arithmetic is uglier but the principle is the same: each payment compounds for however many years remain. A contribution made in year one has 29 more years to work than one made in year thirty, which is why early payments matter so disproportionately.
Divide 72 by your annual return and you get roughly the number of years for money to double.
It is an approximation, but it is accurate enough for mental arithmetic and it makes the cost of a lower return obvious. Dropping from 7% to 5% does not cost you two-sevenths of your money. It adds four and a half years to every doubling.
Two savers, both retiring at 65.
Anna invests £200 a month from 25 to 35, then stops completely. She contributes £24,000 in total.
Ben starts at 35 and invests £200 a month until 65. He contributes £72,000 — three times as much.
At 7% a year, Anna ends up ahead. Her ten years of contributions had thirty additional years to compound, and thirty years is roughly three doublings.
This is not an argument for stopping at 35. It is an argument that the years you cannot get back are worth more than the pounds you can.
Everything above works in reverse for costs. A 1% annual fee does not cost you 1% of your final pot — it compounds against you for the whole period.
On a £100,000 pot over 30 years at 7%, the difference between paying 0.25% and 1.25% in total charges runs to well over £100,000 of final value. That is why platform and fund charges deserve more attention than they usually get, and why the cheapest sensible option is often the right one.
Cash in a current account. Money earning nothing compounds at zero.
Anything you withdraw. Compounding needs the returns to stay in the pot. Taking the growth out each year converts it back into simple interest.
Guaranteed returns. Investment returns are not smooth 7% steps. Real markets deliver a scattered sequence of good and bad years that averages out only over long periods, and the average is not promised.
Inflation-adjusted terms. A 7% nominal return with 3% inflation is roughly 4% in real purchasing power. Both numbers are true; only one of them buys things. Our guide to what inflation does to savings draws that gap out.
Start earlier than feels comfortable, even with an amount that feels too small to matter. Automate it so the decision is made once rather than monthly. Keep total costs low, because they compound against you with exactly the same force. And leave it alone — the curve only pays out to people who stay in it.
For a specific target with a deadline attached, the savings goal and sinking funds tracker does the monthly arithmetic for you.
If you are working out where to put the money, how to start investing in the UK covers the order of operations, and the investment platform comparison covers what each provider charges.