Interest calculated on the balance, not on what you put in
Compound interest is interest that earns interest. Each period, the rate is applied to the current balance, and because that balance includes everything already earned, each period adds slightly more than the one before it.
Simple interest, by contrast, is always worked out on the original sum. Put a thousand pounds at five per cent simple and it adds fifty pounds a year, every year, forever. Compound it and the second year earns five per cent of £1,050, the third of £1,102.50, and so on.
Over two years those are nearly identical. That is the trap: the mechanism looks unimportant exactly when people are deciding whether to bother.
The rule of 72, which is worth memorising
Divide 72 by the annual rate and you get roughly how many years the money takes to double.
- At 6 per cent, 72 over 6 is 12 years. The exact answer is 11.9.
- At 3 per cent, 24 years.
- At 9 per cent, 8 years.
- At 2 per cent, 36 years, which is why an ordinary savings account never feels like it is compounding.
It is an approximation and it is accurate enough between about 4 and 12 per cent to be used in your head during a conversation, which is the entire point of it. It also works on debt, where it tells you how fast something you are ignoring doubles.
Time does more work than rate
Given a choice between a better rate and more years, the years win, and not narrowly. Growth is exponential in time and much closer to linear in the rate over any period you would actually consider, so an extra decade generally beats an extra percentage point.
Which is the real argument for starting a pension early rather than waiting until the contributions can be larger. Money paid in during your twenties has the longest to compound and ends up carrying a disproportionate share of the final pot, and no amount of catching up later buys those years back.
How often it compounds, and why AER exists
The same nominal rate compounded monthly produces a little more than compounded annually, because each month the interest starts earning on itself sooner. The effect is modest and it is real.
That is what AER is for: it restates any account on an annual basis so two products with different compounding frequencies can be compared honestly. When you are choosing between savings accounts, the AER is the comparable number and the headline rate is not.
It runs in both directions
The same arithmetic that grows savings grows debt, and on debt it usually compounds more often. A credit card charging interest monthly on a balance that already includes last month's interest follows exactly the curve above.
It is also why the annual figure quoted on a card is higher than twelve times the monthly rate: the compounding is baked into it. An unpaid balance does not creep, it accelerates, and the acceleration is invisible for the first few months in exactly the way the savings curve is.
Putting numbers on your own case
The compound interest calculator takes a starting balance, a contribution and a rate and shows the year the pot starts earning more than you pay into it, which is the moment the curve above becomes something you can feel. It also handles the question backwards, from a target you want to hit.
On the debt side, the credit card payoff and debt payoff planner run the same maths against you, and the mortgage overpayment calculator shows what shortening the term is actually worth.
Common questions
What is the difference between simple and compound interest?
Simple interest is always calculated on the original amount, so it adds the same sum every year forever. Compound interest is calculated on the balance, which includes the interest already added, so each year earns slightly more than the last. Over a year or two the difference is barely visible. Over twenty or thirty it is the difference between a straight line and a curve that runs away from it.
What is the rule of 72?
A mental shortcut for how long money takes to double: divide 72 by the annual percentage rate. At 6 per cent, 72 divided by 6 gives 12 years, and the exact answer is 11.9, so it is close enough to be genuinely useful without a calculator. It works well for rates roughly between 4 and 12 per cent and drifts at the extremes. It is just as useful in reverse for debt, where it tells you how quickly something you owe doubles if you ignore it.
Does it matter how often interest is compounded?
Yes, though less than most people expect. The same nominal rate compounded monthly produces slightly more than compounded annually, because each month the interest starts earning on itself sooner. That is exactly why AER exists: it restates any account on an annual basis so two products with different compounding frequencies can be compared honestly. If you are choosing between accounts, compare the AER rather than the headline rate.
Is it better to have a higher rate or more time?
Time, comfortably, and it is not close over long periods. Growth is exponential in the number of years and much closer to linear in the rate, so an extra decade generally beats an extra percentage point. This is the whole argument for starting a pension early rather than waiting until you can afford to contribute more: the contributions made in your twenties have the longest to compound and end up doing a disproportionate share of the work.
Does compound interest work against me on debt?
The same maths, pointed the other way, and usually compounded more often. A credit card charging interest monthly on a balance that includes last month’s interest grows the same curve your savings would, which is why an unpaid balance accelerates rather than creeping. It is also why the annual figure quoted on a card is higher than twelve times the monthly rate: the compounding is already in it.
Why does my savings account not seem to compound much?
Usually because the rate is low and the time is short, which is precisely where compounding is least impressive. At 2 per cent it takes roughly 36 years to double, so a couple of years in an ordinary account looks almost exactly like simple interest. The curve only becomes visible when the rate and the years are both meaningful, and noticing that early is worth more than chasing a fraction of a per cent.