Compound interest is often called «the eighth wonder of the world». In one line: it’s interest that starts earning more interest. Given some time, this turns modest contributions into surprising sums. But there’s a side almost no calculator shows — inflation — and we put it front and centre.
What compound interest is
With simple interest, the interest you earn is set aside and doesn’t grow. With compound interest, each bit of interest is reinvested and earns interest in turn. It’s the difference between growth in a straight line and growth that accelerates.
An example: €1,000 at 5% earns €50 the first year. With simple interest, next year you again earn €50. With compounding, the second year’s 5% is on €1,050, so €52.50. Tiny at first — but it builds, and after twenty years the gap is huge.
The calculator
Put in your numbers. The one thing we don’t suggest is the return: type the assumption you want to test. And look at the two figures at the top — the amount «on paper» and what it’s worth in today’s money.
The formula (and how to redo it in Excel or Sheets)
=FV(5%/12, 12*20, -100, -10000, 0) → 68,230Why it feels disappointing at first
Compound growth is not linear: the curve starts almost flat, then shoots up. In the early years the results are small and it’s tempting to quit — the «valley of disappointment». But it’s the patience of those early years that builds the base on which the snowball later takes off.
Most of compound interest arrives at the end. Those who quit early never see it.
The decisive factor: time
In the calculator, try changing only the duration: you’ll see that adding years matters more than adding contributions. Time is the most powerful ingredient, because it’s what gives interest the room to earn more interest. That’s why, in finance, «when you start» often weighs more than «how much you put in».
The other side: inflation
Here’s the part almost no calculator shows. €100,000 in thirty years will not have the same purchasing power as €100,000 today: inflation, year after year, erodes what it buys. Our calculator discounts the inflation you choose (2% is the ECB target) and gives you the amount also in today’s money. That’s the honest number: what matters isn’t the nominal figure, but what you’ll actually do with it.
Does a government bond or a deposit account compound?
Many people wonder, and the answer is surprising: on their own, often not. Compound interest only kicks in when the interest is reinvested — not when it lands in your account and you spend it.
A government bond like a BTP pays periodic coupons, credited to your account. If you cash them and use them, it’s simple interest: the capital doesn’t grow and the coupon stays the same. It becomes compound only if you reinvest each coupon — exactly the difference between the two lines in the chart above, the dashed one (you spend the coupons) and the solid one (you reinvest them).
A deposit account depends on the contract: if the interest stays in the account and earns in turn (capitalised), it compounds; if it’s credited and you withdraw it, it doesn’t.
The only things that compound on their own, without you doing anything, are instruments that pay no coupon to spend: zero-coupon securities (T-bills, or a zero-coupon bond — the gain is already in the discount on the price) and accumulating funds and ETFs, which reinvest everything internally.
One last bit of honesty: even reinvesting, you may not find the same rate again. That «4%» you reinvest today might only be 2% tomorrow — and then the real compounding is less than hoped. It’s called reinvestment risk: it’s why a bond’s «yield to maturity» is a conditional promise, not a certainty.
It also works against you
Compound interest is a neutral force: it also accelerates debt. A credit-card balance or a high-rate loan compound against you with the same maths. Understanding compounding serves both to make it work for you and to avoid being crushed when it plays against you.