How compound interest works (and why starting early wins)

Saving & investing · 6 min read

Albert Einstein supposedly called compound interest "the eighth wonder of the world." Whether or not he really said it, the maths behind it is the closest thing personal finance has to magic: money that earns returns, on returns, on returns. Understanding it is the single biggest mindset shift for anyone saving or investing.

Simple vs compound interest

With simple interest you earn a return only on your original sum. Put £10,000 in at 5% and you get £500 a year, every year. With compound interest, each year's return is added to the pot, so the next year you earn a return on a bigger balance. Year one is still £500, but year two earns 5% of £10,500, and so on. The gap looks small at first and then becomes enormous.

The formula

A = P × (1 + r/n)^(n·t)

A — the final amount
P — the starting principal
r — the annual interest rate (as a decimal)
n — how many times a year interest is compounded
t — the number of years

The two levers people underrate are t (time) and n (frequency). The longer the money compounds, and the more often, the more dramatic the result.

The rule of 72

A handy shortcut: divide 72 by your annual return to estimate how many years it takes your money to double. At 6% a year, money doubles roughly every 12 years (72 ÷ 6). At 9%, every 8 years. It isn't exact, but it's close enough to do in your head — and surprisingly motivating.

Why starting early beats saving more

Time is the most powerful ingredient — more than the amount you save or even the rate you earn.

Saver A invests £200 a month from age 25 to 35 (ten years, £24,000 in total), then stops and never adds another penny.

Saver B invests £200 a month from age 35 all the way to 65 (thirty years, £72,000 in total).

At a 7% average return, Saver A often ends up with more at 65 — despite paying in a third of the money — purely because their early contributions had an extra decade to compound.

See it grow

Compound Interest Calculator

Enter a starting amount, regular contributions and a rate to see year-by-year growth — and watch how time changes everything.

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Regular contributions

Most people don't invest a lump sum and walk away — they add a bit each month. Those steady contributions compound too, and because you're buying in across the ups and downs of the market, you smooth out the timing risk of investing everything at once. Consistency tends to beat trying to pick the perfect moment.

The inflation caveat

One honest note: a 7% return doesn't mean 7% more spending power. Inflation erodes the value of money over time, so what matters is your real (after-inflation) return. Compounding still wins handsomely — but think in terms of returns above inflation, not the headline number.

Common mistakes

Waiting "until you can afford more." A small amount started now usually beats a larger amount started in ten years. Time is the lever you can't get back.

Interrupting the compounding. Dipping into invested savings resets the snowball; leaving it untouched is where the magic happens.

Ignoring fees. A 1% annual fee doesn't sound like much, but compounded over decades it can quietly consume a large share of your final pot.