How compound interest actually works

Say you put £1,000 in a savings account paying 5% a year. How much is it worth in ten years? Most people guess somewhere near £1,500 — the £1,000 plus £50 a year, ten times over. The real answer is £1,629. The extra £129 is the whole point of compound interest, and once you see where it comes from, you understand most of how money grows or buries you [5].

Interest, the simple version first

Interest is the price of money. When you save, the bank pays you interest for letting it use your money. When you borrow, you pay interest for using someone else’s [2][10].

There are two ways to count it. Simple interest is calculated only on the original amount — the principal [1]. Put £1,000 in at 5% simple interest and you earn £50 every year, flat, forever. After ten years you’ve earned £500, so you have £1,500. Each year is identical because the £50 is always 5% of the same £1,000 [6].

Car loans and many short personal loans work this way [6][13]. The interest is figured on what you originally borrowed, not on a growing pile.

Where compounding comes from

Compound interest is interest on your interest [19]. The difference is one rule: each year, the interest you earned gets added to the base, and next year you earn interest on that bigger base too [5][15].

Walk the £1,000 at 5% through it, year by year:

• Year 1: 5% of £1,000 = £50. Balance £1,050.
• Year 2: 5% of £1,050 = £52.50. Balance £1,102.50.
• Year 3: 5% of £1,102.50 = £55.13. Balance £1,157.63.

Notice the interest payment grows each year — £50, then £52.50, then £55.13 — even though the rate never changes. That’s because the base it’s charged on keeps getting bigger. By year ten the balance is £1,629, and that final year alone added about £78, against the £50 the first year added [5].

The formula is just that rule written compactly: final amount = principal × (1 + rate)^years. The “to the power of years” part is the compounding — it’s the same 1.05 multiplied by itself once for each year [3]. You don’t need to do the algebra by hand. You need to understand that the exponent is what makes the line curve upward instead of running straight.

How often it compounds changes the answer

We assumed the interest gets added once a year. Often it’s added more frequently — monthly, daily — and the more often it compounds, the more you earn, because each chunk of interest starts earning sooner [24].

The gap is small at everyday rates. £1,000 at 5% compounded once a year gives £1,050 after a year. Compounded monthly, it gives about £1,051.16. A pound or so — not life-changing on a savings account [3].

It matters far more when the rate is high. That’s the bridge to the dangerous side.

The same engine, running against you

Compound interest does not care which direction it runs. On a credit card, you are the one paying interest on interest [15].

Here’s the mechanism on a card: if you don’t clear the full balance, the interest charged gets added to what you owe, and next month you’re charged interest on that larger balance — interest on interest, compounding against you [15]. Cards also typically compound daily, and they quote an APR — the annual percentage rate, the yearly cost of borrowing — that can sit around 20% or more [15].

Run £1,000 of card debt at 20% with no payments. Simple interest would add £200 a year. Compounded daily, the real cost over a year is closer to £221 — and it keeps accelerating if you leave it [15]. Now flip back to the savings example: your money grew at 5%, your card debt grows at 20% or more. The same engine, four times as fast, pointed the wrong way. This is why a balance you carry on a card can outrun almost anything a safe account pays you.

The Rule of 72 — doubling in your head

There’s a shortcut for feeling compounding without a calculator. The Rule of 72: divide 72 by the annual rate, and you get roughly how many years it takes the money to double [7][8].

• At 6%, money doubles in about 72 ÷ 6 = 12 years.
• At 9%, about 8 years.
• At 3%, about 24 years.

It’s an approximation, not exact — it works best for rates in the single-digit-to-low-teens range, and there’s a close cousin, the Rule of 70, used for the same trick [12][9]. But it’s good enough to reason with. And it runs both ways: a 20% card debt left alone doubles in roughly 72 ÷ 20 ≈ 3.6 years [8].

Why starting early beats saving more

The slow start is what fools people. In the £1,000 example, the first year added £50 and the tenth added £78 — but stretch it to forty years and the curve goes near-vertical at the end. The interest earned in the final decade dwarfs everything before it, because the base it’s working on is so much larger [11].

That’s why time is the lever that matters most. A person who saves a modest amount in their twenties and then stops can end up ahead of someone who saves far more but starts in their forties — the early money simply had more years to compound [11]. The amount matters; the years matter more.

The common mistakes

Reading the rate as the only number. People compare 5% here against 6% there and miss that time and compounding frequency are doing much of the work. A lower rate left alone for longer can beat a higher rate cashed out early [11].

Thinking a 20% APR costs 20%. With daily or monthly compounding, the real annual cost of card debt is higher than the headline APR [15].

Underrating small, regular amounts. A small sum added every month, left to compound, becomes large on a timescale that surprises people — because each contribution starts its own compounding clock [4].

What varies

Rates change — savings rates, card rates, the lot — and the figures here are illustrative, not promises. Inflation, the steady rise in prices, quietly eats into what your savings can buy, so a 5% return when prices rise 2% is really closer to 3% of true growth [20][29]. Investment returns aren’t fixed like a savings rate; they swing, and past returns are not a guarantee of future ones [14]. The mechanism is durable; the numbers depend on you, your country, and the moment.

The one thing to carry: compound interest is interest on interest, and the base keeps growing — so time, not just the rate, decides where you end up. It builds wealth slowly then suddenly, and it buries debt the same way.