Guide

Compound interest, demystified

Everyone has heard of it; few have looked at the mechanism closely. It is not a magic formula — it is repeated multiplication, and almost all of it happens at the end.

By Mohamed ATIA·Updated 20 August 2026

The principle in one sentence

Compound interest is interest that earns interest. You invest €1,000. At 7 %, the first year earns you €70. The second year, the 7 % no longer applies to €1,000 but to €1,070: it earns €74.90. The gap looks trivial. It is anything but, thirty years later.

That is the whole difference with simple interest, where only the original capital works. Over thirty years at 7 %, simple interest turns €1,000 into €3,100. Compound interest turns it into €7,610. The formula is always the same:

final capital = initial capital × (1 + rate)^number of years

That exponent is the only thing that really matters. A rate enters the calculation once; time enters it as many times as there are years.

Why time beats the amount

The consequence is counter-intuitive, and it is what makes the subject interesting: starting early matters more than contributing heavily.

Take two people aiming at retirement at 65, with the same 7 % annual return.

Profile	Contributes	For	Total paid in	At 65
Starts at 25	€150 / month	40 years	€72,000	≈ €371,000
Starts at 40	€300 / month	25 years	€90,000	≈ €235,000

The second person pays in 25 % more and ends up with 37 % less. Fifteen years of head start did more than €18,000 of extra contributions. It is the only serious argument for starting now, however small the amount, however imperfect the plan.

The rule of 72. To find how many years a sum takes to double, divide 72 by the rate. At 7 % it doubles in a little over ten years. At 3 % it needs twenty-four. It is an approximation, but a very close one.

What thirty years of markets actually show

The examples above assume a steady return. Markets never deliver one. This is the part most simulators quietly skip.

Over 1995–2025, the MSCI World index returned 8.46 % a year as a geometric average: 100 invested at the start of 1995 was worth roughly 1,241 at the end of 2025, net dividends reinvested, in dollars. A remarkable return — earned by living through eight negative years out of thirty-one, including a fall of more than 40 % in 2008.

Put differently: the average rate was never any single year's rate. Nobody made 8.46 % in 2008. The average is the destination, not the road.

Two effects the formula ignores. First inflation: a 7 % return with 2 % inflation is about 4.9 % of purchasing power gained, not 5 % — and that gap compounds too. Second tax: depending on where you live, the same gross performance leaves you between 100 % and 59 % of the gain. That is the subject of our European tax comparison.

The three mistakes that break the mechanism

1. Interrupting. Selling after a fall does more than crystallise the loss: it resets the exponent. A portfolio that sits out the ten best trading days of a decade loses a disproportionate share of its performance, because those days almost always follow the worst ones.

2. Paying too much in fees. Annual fees of 2 % instead of 0.2 % do not cost you 1.8 %: they compound in the opposite direction. Over thirty years they absorb a considerable share of the final capital. That is the entire point of index ETFs, whose ongoing charges run from 0.07 % to 0.40 % a year.

3. Ignoring your country's tax rules. An annual tax on assets — as in the Netherlands or Switzerland — does not compare to a one-off tax at exit, even at a higher headline rate. The first eats into the base that compounds, every single year.

Run the numbers on your own case

Averages are only useful against a real situation. Cumulo's calculator takes your starting capital, your contributions, your horizon and your country of residence, then shows the result net of tax and inflation — along with how much of the final capital came from your contributions and how much from interest.

Open the calculator

Frequently asked questions

What is the compound interest formula?

Final capital = initial capital × (1 + rate)^number of years. With regular contributions, you add each contribution compounded over its own remaining time. The rate enters the calculation once, time enters it as many times as there are years, which is why the horizon weighs more than the amount.

How much does €10,000 grow to over 20 years?

At 7 % a year, €10,000 becomes roughly €38,700 in twenty years, before tax and inflation. At 5 %, about €26,500. At 3 %, about €18,100. The spread between those three results is far wider than the spread between the rates themselves: that is the exponent at work.

What is the rule of 72?

It gives the doubling time of a sum: divide 72 by the annual rate. At 6 %, capital doubles in about twelve years; at 8 %, in nine. It is an approximation, but very close to the exact calculation for rates between 2 % and 12 %.

Does compound interest still work when markets fall?

The mechanism is the same but works against you: a 50 % fall requires a 100 % rise to get back to where you started. That is precisely why duration and consistency matter more than trying to enter at the right moment.