What is compound interest?

Compound interest means that the returns an investment earns are added to it and then earn returns of their own: growth builds on growth. In the first years the effect is barely visible; over decades it becomes the dominant force in how wealth grows — which is why time in the market matters more than almost anything else.

For investments, the same principle applies to reinvested dividends and rising prices, and it is usually simply called compounding.

The formula

A starting amount $V_0$ growing at a rate $r a$ year for $n$ years reaches:

V_n = V_0 \, (1 + r)^n

With a regular contribution $C$ at the end of each year, the future value of the contributions is added:

V_n = V_0 \, (1 + r)^n + C \, \frac{(1 + r)^n - 1}{r}

A simple illustration

€10,000 invested at 7% a year and left untouched grows as follows:

Years	Value	Of which growth
10	€19,672	+9,672
20	€38,697	+28,697
30	€76,123	+66,123
40	€149,745	+139,745

€10,000 at 7% a year. The growth curve steepens as the gains start earning gains of their own.

In the first ten years the money roughly doubles. In the last ten years alone it grows by more than €73,000 — over seven times the original investment — without any new money. With simple interest, paid only on the original amount, the same €10,000 would have reached just €38,000 after 40 years.

Why time matters most

Two savers each invest €2,400 a year — €200 a month — at 7%:

The first starts at 25 and stops at 35: ten years, €24,000 invested, then left to grow.
The second starts at 35 and continues until 65: thirty years, €72,000 invested.

At 65, the first saver has about €252,000 and the second about €227,000. The early saver ends with more, having invested a third as much, because each of their euros had thirty extra years to compound.

What works against it

Costs: every percentage point of fees compounds too, in the other direction.
Taxes: taxes paid on returns every year reduce the amount that keeps compounding.
Inflation: growth measured in euros overstates the growth of purchasing power.
Interruptions: withdrawing money, or selling in a downturn, resets part of the compounding.

The rule of 72 gives a quick feel for compounding: dividing 72 by the yearly return gives roughly the number of years it takes money to double.

A worked example

Worked through on a sample portfolio. The figures below are that portfolio’s, not yours.

How much difference does reinvesting dividends make over time?

I can explain this clearly without numbers.

What reinvesting dividends does

Reinvested dividends buy more shares immediately, so those extra shares also pay dividends later. That creates compounding: dividends generate dividends over time.
Taking dividends as cash stops that compounding unless you put the cash back to work; cash held outside the investment typically compounds slower or not at all.
The gap between reinvesting and taking cash grows with higher dividend yield, longer holding periods, and stronger price growth. Fees, taxes and any interest the cash earns reduce that gap.

How to see the effect for you

I can run a side-by-side calculation using your actual portfolio and show the end values and the difference, with clear assumptions (holding period, whether cash earns interest, taxes, fees).
The simulation will state all assumptions it uses.

If you want, I’m happy to run that comparison for your portfolio now.

See these numbers for your own portfolio

Floreo works out every figure on this page from your own holdings — returns, risk, allocation, currencies — and the assistant explains them the way this page does. Import from your broker, or try it on the sample portfolio first.

Start Demo

The demo opens straight away on a sample portfolio — no account needed.