An apple tree gives apples. If you eat them, next year you will have the same. If you plant the seeds, in a few years you will have several trees, and each will give apples and seeds to plant more. That is compound interest: what you earn is not spent, it is planted, and it starts earning on its own.
Simple and compound interest
With simple interest only the money you put in at the start earns. With compound interest the gains from previous years earn too, because they are reinvested.
Put 10,000 euros at 7% a year for 30 years. With simple interest you earn 700 euros every year, always the same, and end up with 31,000. With compound interest you earn 700 the first year, 749 the second because the first 700 are now earning too, and so on: you end up with 76,122.55 euros. Same money, same rate, more than double.
The difference is time. In the formula, years do not add: they are the exponent. Each year that passes does not add the same as the one before, it adds more.
With a small amount every month
Most people do not start with 10,000 euros but by setting aside an amount every month. This is what 200 euros a month gives at an assumed return of 7% a year, reinvesting everything:
| Years | You put in | You have |
|---|---|---|
| 10 | €24,000 | €34,616.96 |
| 20 | €48,000 | €104,185.33 |
| 30 | €72,000 | €243,994.20 |
| 40 | €96,000 | €524,962.68 |
Look at the last two rows. Between year 30 and year 40 you put in 24,000 euros more, the same as in the first decade, and the total goes from 243,994.20 to 524,962.68. Those last ten years produce more than the previous thirty put together.
Starting earlier beats putting in more
Two people want to retire at 65. The first starts at 25 with 200 euros a month. The second waits until 35 and, to make up for it, puts in twice as much, 400 euros a month. At the same 7%, the first ends up with 524,962.68 euros. The second, with 487,988.40. She has put in 144,000 euros against 96,000, and still ends up with less.
Those first ten years cannot be made up with money, because what the first person has is not more money, it is more time. That is why the best amount to start with is one you can keep up every month, however small, and the best time is this month.
The rule of 72
To work out in your head how long money takes to double, divide 72 by the annual return. At 7%, about 10 years; at 4%, 18. The exact figure at 7% is 10.24 years: the rule is an approximation, but good enough to compare.
It also works the other way. If inflation is 4%, prices double in about 18 years, and what you have in the bank buys half.
Benjamin Franklin did the sums
Benjamin Franklin died in 1790 and left 1,000 pounds to the town of Boston and another 1,000 to Philadelphia, to be lent to young craftsmen at 5%. Whatever was repaid would be lent again, for two hundred years. He wrote down the sums: after a hundred years there would be 131,000 pounds, and after two hundred, 4,061,000. The arithmetic was right.
Reality was less obliging. In 1907 the Philadelphia fund stood at 172,350 dollars, less than a quarter of what he had projected, and in 1990 at just 2 million. Boston’s, which gave up the loans and moved into the stock market, reached almost 5 million. Franklin’s sums were optimistic, partly because the apprenticeship and trades system he had come from himself disappeared.
The lesson holds today: the formula does its job only if the return holds up year after year. That is why where you put your money matters so much, and why a fixed-interest loan, which depends on the borrower paying, is not the best seed. We explain it in The safest investment there is.
It also works against you
Fees. With the same 200 euros a month for 30 years and a 7% gross return, if you pay 0.1% a year you end up with 239,234.07 euros. If you pay 1.5%, with 182,722.38. The difference, 56,511.69 euros, has gone to the fee, compounded too.
Inflation. The European Central Bank’s stated target is for prices to rise 2% a year. Sustained for 30 years, that leaves 10,000 euros sitting in the bank buying what 5,520.71 buy today. You lose almost half without doing anything, because the euro’s loss of purchasing power compounds too. We explain it in What inflation is and why it happens.
How to put it to work
Three things, in this order: a fixed amount every month that you can keep up for years, invested in real assets that grow over time, such as companies or an index fund or ETF, and low fees. Then patience. Most of the work is done by the last years, and they only come if you do not stop in the first ones.
You can try your own numbers in the compound interest calculator. And if you are starting from scratch, the steps in order are in Start investing from scratch.
Educational content. Not personalised financial advice. The 7% is an assumption to explain the mechanism, not a promised return: real returns change every year and past performance does not guarantee future results.