Compound interest explained with examples
Compound interest is the one personal finance formula that is genuinely worth understanding. Not because it is complicated. Because the result does not look like what your intuition says.
What it is exactly
Simple interest means earning interest only on what you put in. Compound interest means also earning interest on the interest you have already earned.
With €10,000 at 5%, you earn €500 the first year. The second year you do not earn another €500, you earn 5% of €10,500, which is €525. The third, 5% of €11,025. The difference looks small at first. It stops being small after year ten.
The formula is capital times (1 + rate) to the power of the number of periods. What matters in that formula is not the rate but the exponent. Time is what multiplies.
€200 a month at 5%: the three horizons
Let us fix a realistic contribution, €200 a month, and an average annual return of 5% net of fees. That is a conservative figure for a diversified long-term portfolio, although no single year looks like the average.
In each scenario you have put in the same money per month. What changes is how much it has worked for you.
- 10 years: you contributed €24,000 and have about €31,000. Interest is €7,000.
- 20 years: you contributed €48,000 and have about €82,000. Interest is €34,000.
- 30 years: you contributed €72,000 and have about €166,000. Interest is €94,000, more than everything you put in.
The price of starting late
Compare two people. Ana starts at 25 with €200 a month and stops at 35. She contributes for only ten years, €24,000 in total, and leaves the money untouched until 65.
Luis starts at 35 with the same €200 and does not stop until 65. He contributes for thirty years, €72,000.
At 5%, Ana reaches 65 with about €134,000. Luis, with about €166,000. Luis put in three times the money to end up with 24% more. Ana's first ten years were worth almost as much as Luis's thirty.
That is the part nobody explains well: starting late does not mean earning a little less. Every year you delay is paid for with the years of highest growth, which are always the last ones.
Fees compound too
The same mechanism that multiplies your interest multiplies what you are charged. A 1.5% annual fee on a 6.5% gross return leaves you at 5%. A 0.2% fee leaves you at 6.3%.
With €200 a month over 30 years, that difference between 5% and 6.3% is about €45,000 less in your account. You never see it on a statement because it never arrives.
That is why a product's annual cost is the second most important figure after the time horizon. And why it pays to look at the total expense ratio, not just the management fee.
How to use it without going mad
You do not need to guess the rate. You need the contribution to be automatic and the horizon to be long. A standing order on payday does more than any analysis.
And if you are self-employed with irregular income, the contribution can be a percentage of each payment rather than a fixed figure. Compound interest does not distinguish between a fixed €200 and an average €200.
Frequently asked questions
What return is reasonable to use in the calculator?
For a diversified long-term equity portfolio, 4% to 6% a year net of fees and inflation is a prudent assumption. For a savings account, whatever rate you are offered today.
Is it better to contribute monthly or once a year?
Monthly. Each contribution starts compounding sooner and you avoid the risk of putting everything in at a bad moment.
Does inflation not eat all of this?
It eats part of it. At 2% inflation, the €166,000 after 30 years is worth about €92,000 in today's money. Still far more than the €72,000 you put in, and vastly more than cash would have left you.