Compound interest is the idea that your money earns money, and then that money earns money too. It's often described as if it were magic. It isn't. It's arithmetic that's slow to start, which is exactly why people give up on it before it gets going.
Simple interest first
Put £1,000 in an account paying 5% a year in simple interest and you earn £50 a year, every year, on the original £1,000. After 20 years you'd have £2,000: your £1,000 plus 20 lots of £50.
That's the slow, straight-line version. Very few savings accounts work like that.
Now compound it
With compound interest, the interest is added to your balance, and next time interest is worked out on the bigger balance. Year one, you earn interest on £1,000. Year two, on £1,000 plus year one's interest. And so on.
Take the same £1,000 at 5% a year, with interest added monthly. After one year it's about £1,051. After ten years, about £1,647. After 20 years, about £2,713. After 30, about £4,468.
Look at the gaps. The first ten years add about £647. The second ten add about £1,066. The third ten add about £1,755. Same rate, same starting money, and each decade adds more than the one before, because each one starts from a bigger number.
That's the whole trick. The rate matters, but time matters more, because the growth keeps growing.
Adding a bit each month
Most people don't put in a lump sum and walk away. They add something every month. Here's what that looks like with £1,000 to start and £100 a month, at 5% a year:
| After | Paid in | Growth | Total |
|---|---|---|---|
| 1 year | £2,200 | £79 | £2,279 |
| 5 years | £7,000 | £1,084 | £8,084 |
| 10 years | £13,000 | £4,175 | £17,175 |
| 20 years | £25,000 | £18,816 | £43,816 |
In year one, growth is a rounding error: £79. By year 20, growth is £18,816, and it's doing nearly as much work as you are. Most of that growth arrived in the second decade.
The same maths explains why starting earlier matters so much. £100 a month at 5% for 40 years comes to about £152,600, from £48,000 paid in. Start ten years later and do the same for 30 years, and it's about £83,200 from £36,000. Ten fewer years, £12,000 less paid in, and almost £70,000 less at the end.
A quick way to estimate it
There's an old shortcut called the rule of 72: divide 72 by the yearly rate, and you get roughly how many years it takes for money to double. At 4%, that's about 18 years. At 7%, about 10.
It's an estimate, not a law. With interest added monthly, the exact answers are about 17.4 years at 4% and 9.9 years at 7%. Close enough for a napkin, and a handy check on anyone promising your money will double by Christmas.
Try your own numbers
- Final value
- £43,816
- Total paid in
- £25,000
- Growth
- £18,816
These are the figures for the starting numbers. The calculator needs JavaScript to update them.
Interest is added monthly at the yearly rate divided by 12. Monthly additions go in at the end of each month. No tax, fees or inflation, and the same rate every year, which real investments never manage.
It works on debt too
Compound interest doesn't care whose side it's on. On a debt you're not paying off, interest is added to the balance, and then charged on the new balance.
£1,000 owed at 20% a year, with interest added monthly and nothing paid, becomes about £1,219 after a year. That's why the FCA says the interest on most short-term debt is likely to be many times higher than the return on any investment. Clearing expensive debt is compounding in your favour, with no risk.
Fees and tax compound too
Anything that takes a slice every year takes a slice of the growth as well, and of the growth on that growth. A yearly fund charge of 1% doesn't cost you 1% of your money. Over decades, it costs you far more than that, because the money it removes would have compounded too.
Try it in the calculator. £100 a month for 20 years at 5% ends at about £41,100. At 4%, as if charges took an extra point a year, it's about £36,700. The FCA warns that charges can mount up over time and eat into your returns.
Tax works the same way. Savings interest above your Personal Savings Allowance, which is £1,000 a year for basic-rate taxpayers and £500 for higher-rate, is taxed. Inside an ISA there's no tax on interest, income or gains, so the whole return stays in to compound.
The honest caveats
The calculator uses one steady rate, every year. Savings rates change, and investments don't grow in a straight line at all. Some years they fall.
Investments can fall in value, and you could get back less than you put in. A 5% rate in a calculator is an illustration. It isn't a forecast or a promise.
The FSCS can't accept claims for poor investment performance. The FCA's guidance is that the higher the potential return, the greater the danger of things going wrong, and that investing over at least five years gives you more chance to ride out dips.
The calculator also ignores inflation. £43,816 in 20 years won't buy what £43,816 buys today. That doesn't make compounding less useful. It just means the number at the end is in future pounds.
What compounding rewards, above all, is leaving things alone. The FCA notes that staying invested rather than moving in and out helps keep costs down. The hard part isn't the maths. It's the waiting.