Compound interest explained: formula, rule of 72, examples

What is compound interest?

With simple interest you earn interest only on your original amount. With compound interest your earnings stay in the pot and earn returns of their own the following year.

An example: you invest 10,000 € at 6 % a year.

Example calculation, rounded, no guarantee.

Look at the right-hand column. After ten years the gap is still small. After 30 years compounding has created more than twice as much. Picture a snowball rolling downhill: the bigger it gets, the more snow sticks with every turn. The length of the slope is how long you stay invested.

With shares and ETFs, people speak of the compounding effect. There is no fixed rate, but price gains and reinvested dividends keep growing in exactly the same way.

How to calculate compound interest: the formula

For a one-off investment:

Final amount = starting amount × (1 + interest rate)^years

The rate goes into the formula as a decimal, so 0.06 for 6 %. Using the numbers above: 10,000 € × 1.06³⁰ = around 57,400 €.

Compound interest with monthly savings

With a savings plan the calculation gets longer, because each payment grows for a different length of time. The first payment works for 30 years, the last for one month. The easiest way is the savings plan calculator. For a quick estimate, here is what 100 € a month can become:

Example with monthly compounding, before costs and taxes, rounded. For your amount: value × amount ÷ 100. Example: 250 € over 30 years at 6 % ≈ 2.5 × 100,452 € ≈ 251,000 €.

The rule of 72: doubling in your head

How long until your money doubles? Divide 72 by your annual return in percent:

It's an approximation, but a remarkably good one. And it reveals something striking: start at 31 and, at 6 %, your money doubles three times by 67. 1 € becomes 8 €. Start at 43 and it doubles only twice: 1 € becomes 4 €. Starting twelve years earlier means twice as much from every euro.

Compounding in practice: starting early beats paying in longer

Back to the two people from the start. Greta and Ben are made up; the maths is real. Both save 200 € a month, both at an assumed 6 % a year:

Example calculation, rounded, before costs and taxes, no guarantee.

Greta stops at 35 and never touches her money again. Ben starts exactly then and pays in until retirement. Ben paid in more than three times as much and ends up with only about 9,000 € more. Greta's ten-year head start is worth almost as much as Ben's 32 years of saving.

Why the first years feel so slow

Here is what 200 € a month can become over 40 years:

Example calculation, rounded to thousands, no guarantee. After 40 years you have paid in 96,000 €.

Three things stand out:

1. The first ten years are slow. You've paid in 24,000 € and have around 32,800 €. Compounding has added "only" about 9,000 €.
2. After a little over 20 years the balance tips. From then on compounding contributes more than your own deposits. Your money works harder than you do.
3. The end is huge. In the last ten years the portfolio grows almost as much as in the first thirty combined.

That's exactly why so many people give up in the early years. The reward comes late. Knowing that makes it easier to stick with it.

What does waiting cost?

Flip the question: you want 300,000 € by age 67. How much do you need to save each month?

Assumes 6 % a year, before costs and taxes, rounded. No guarantee.

Every five years the jump gets steeper. At 25, around 130 € a month is enough. At 55, it's more than many people pay in rent. I only got into this topic later in life myself. That's why today I tell everyone to start as early as they can, even with small amounts.

What gets in the way of compounding

Compounding has three opponents. Knowing them gets you noticeably more out of it.

Inflation: nominal isn't real

A 6 % return doesn't mean you can buy 6 % more. With around 2 % inflation, about 4 % is left in real terms. The 200,000 € from the example is worth roughly 139,000 € in today's money after 30 years. Still a lot, just more honestly calculated.

Costs: the silent return killer

Every percent in fees is missing from compounding, year after year. With 200 € a month over 30 years, two percentage points (4 % instead of 6 %) make a difference of around 62,000 €. Broad ETFs often cost only 0.1 to 0.3 % a year, many active funds much more. German consumer advice centres recommend low-cost index funds for exactly this reason (Verbraucherzentrale Hamburg, in German). More in ETF savings plan: how to start in 5 steps.

Debt: compounding in reverse

Compounding works against you too. An example: 3,000 € in an overdraft at an assumed 11 %, without repaying anything and without the interest being paid, grows to around 5,050 € in five years and around 8,500 € in ten. That's why paying off expensive debt comes before investing. No portfolio is guaranteed to earn 11 % a year; clearing the overdraft is.

Example calculations, rounded. Your actual overdraft rate depends on your bank.

What return is realistic?

A broadly diversified global equity index such as the MSCI World has returned roughly 7 to 8 % a year on average over the past 50 years or so, with dividends reinvested. After around 2 % inflation, about 5 to 6 % remains in real terms. That's why I use 6 % in the examples, a cautious assumption for a pure equity portfolio over the long run.

Example calculation, no guarantee.

A long-term average doesn't mean you get that every year. There are years with over 30 % gains and years with clear losses. Plan cautiously and be pleasantly surprised if it turns out better.

Time in the market beats timing the market

Many people think: "I'll wait until prices fall and buy cheaply then." It feels clever. In practice it almost never works.

Anyone who kept 10,000 US dollars invested in the S&P 500 (the 500 largest US companies) from 1996 to 2025 ended up with more than 192,000 US dollars. Missing just the ten best trading days left less than half. According to Hartford Funds, most of the best days came during or right after sharp market drops, exactly when fear is greatest.

Compounding doesn't need the perfect entry point. It needs time during which you stay invested.

What if I'm already 45 or 55?

You have less time, but often other advantages: a higher income, fewer costs for children, maybe a paid-off home.

Example calculations before taxes and costs, no guarantee.

Three levers help when you start later:

• Save more: redirect pay rises or finished loan payments straight into your savings plan.
• Put existing money to work: part of what sits in a current or savings account can be invested long-term once your emergency fund is in place.
• Think beyond retirement day: much of your money often stays invested for years and keeps growing while you withdraw gradually.

And: the shorter the time to your goal, the more you should think about price swings.

Done in 10 minutes

1. Work out your number: enter your amount, years to your goal and 6 % into the savings plan calculator. Then try 50 € more.
2. Check for expensive debt: is an overdraft or credit card in the red? Start there.
3. Start a standing order or savings plan, even with a small amount. Starting matters more than size.
4. Write down one sentence: "Time in the market beats timing." Somewhere you'll see it in the next crisis.

Sticking with it when it feels slow

Compounding rewards you late, with years in between where little seems to happen. What helps is seeing progress without staring at prices every day.

My book "Depot-IQ" explains it all step by step, in plain language, from your first budget to your own portfolio. The English edition is in the works, and the depiq app is coming in English too.

This article is not investment advice. All figures are example calculations. Past performance is no guarantee of future results. Source on timing: Hartford Funds.