Compound interest is returns on your returns. You contribute money, it earns something, and that earned amount then goes on to earn as well. Repeat that for thirty years and the result is hard to grasp with ordinary mental arithmetic.
Two things that rarely appear in the same article: how large the effect really is, and what it can't do. The second is at least as useful.
What is compound interest?
With simple interest you earn a return each year on your original contribution. With compound interest you earn a return on your contribution plus everything you've earned before.
Take €10,000 at 6% a year for thirty years:
- Simple: €600 a year × 30 = €18,000 in interest. Final amount €28,000.
- Compound: €10,000 × 1.06³⁰ = €57,435.
More than twice as much, on exactly the same contribution at the same rate. The €29,435 difference is entirely returns that produced returns.
In investing this happens by itself as long as you withdraw nothing. A price rise increases your total position, and the next rise calculates on that higher amount. Reinvested dividends work the same way. All it requires is keeping your hands off your money.
The two savers
This example is well known, and it stays striking because the outcome looks implausible until you check it.
Two people, both earning 7% a year, both contributing €300 a month.
Anna contributes from age 25 to 35. Ten years, then she stops entirely and leaves it until 65.
Ben starts at 35 and keeps going until 65. Thirty years.
| Anna | Ben | |
|---|---|---|
| Years contributing | 10 | 30 |
| Total contributed | €36,000 | €108,000 |
| Value at 65 | €395,270 | €365,991 |
Anna contributed €72,000 less and ends up with €29,278 more.
She did nothing cleverer than Ben. She was simply earlier. Her money got thirty extra years to multiply itself, and those thirty years at the end are the years when the effect is largest.
The lesson isn't "save for ten years then stop". The lesson is that time is the only factor you can't make up. Returns you can influence. Contributions you can increase. Years that have passed don't come back.
What ten years are worth
More concretely, at €200 a month and 7%:
| Term | Total contributed | Final value |
|---|---|---|
| 20 years | €48,000 | €104,185 |
| 30 years | €72,000 | €243,994 |
| 40 years | €96,000 | €524,963 |
From 20 to 30 years: you contribute half as much again and get more than double. From 30 to 40: you contribute a third more and again get more than double.
The final ten years produce more in absolute euros than the first twenty combined. That's the shape of the curve, and it's also why people drop out halfway: at that point it doesn't feel like anything remarkable yet.
The formula, and how to apply it yourself
One-off contribution
Final capital = contribution × (1 + return)^years
For €10,000 at 6% over 30 years: 10,000 × 1.06³⁰ = €57,435.
Regular contributions
Contributing monthly means each payment counts over its own remaining term:
Final capital = monthly amount × ((1 + r)^n − 1) / r
Where r is the monthly return (annual divided by twelve) and n the number of months.
In Excel or Google Sheets
You don't need to do this by hand. The function is FV, for future value:
=FV(0.07/12, 360, -200, -10000)
Left to right: monthly return, number of months, monthly contribution, starting amount. Contributions and the starting amount are negative because that's money leaving your pocket: the same sign logic as XIRR.
If you'd rather work in years, use =FV(0.07, 30, -2400, -10000). That gives a slightly lower result, because the formula then assumes you contribute once a year rather than monthly.
The rule of 72
For a quick estimate of how long your money takes to double: divide 72 by your return percentage.
| Return | Rule of 72 | Actual |
|---|---|---|
| 3% | 24.0 years | 23.4 years |
| 5% | 14.4 years | 14.2 years |
| 7% | 10.3 years | 10.2 years |
| 10% | 7.2 years | 7.3 years |
Accurate enough for mental arithmetic, and it works both ways. At 3% inflation, the purchasing power of your savings also halves in just over twenty-three years.
What returns can't fix: your savings rate
This is where almost all compound-interest content goes wrong. The message is usually "start early and let it do the work", as though returns play the leading role.
For anyone calculating towards financial independence, that isn't right. Your savings rate, the share of income you set aside, weighs more heavily. And it weighs more for two reasons: it raises what you contribute, and it lowers what you need, because you're living on less.
Take a target of twenty-five times annual spending, at 5% real return, starting from zero:
| Savings rate | Years to target |
|---|---|
| 10% | 51.4 |
| 20% | 36.7 |
| 30% | 28.0 |
| 40% | 21.6 |
| 50% | 16.6 |
| 60% | 12.4 |
Note what happens between 10% and 20%: you don't halve your timeline, but you take nearly fifteen years off it.
And the comparison that makes the point, both starting from a 20% savings rate:
- Raising your savings rate from 20% to 30%: 36.7 → 28.0 years. 8.7 years sooner.
- Raising your return from 5% to 7%: 36.7 → 30.7 years. 6.0 years sooner.
Ten percentage points on your savings rate beats two percentage points of extra return. And the first is entirely within your control while the second largely isn't: earning two points more consistently means taking more risk, which can also go the other way.
Compound interest is an amplifier, not an engine. It multiplies what you put in. Put in little and it multiplies little.
Costs compound in exactly the same way
The same mechanism works against you through costs, and because the percentages are small, it's systematically underestimated.
€100,000, thirty years, 7% gross return:
| Annual costs | Final value |
|---|---|
| 0.2% | €719,677 |
| 0.5% | €661,437 |
| 1.5% | €498,395 |
The difference between 0.5% and 1.5% is €163,041: nearly a quarter of your final capital, given away for one percentage point a year.
When choosing a fund, that percentage feels like a detail. Over thirty years it's the most expensive detail in your portfolio.
And inflation compounds the other way
The least pleasant application. Inflation is compound interest working against you, and it works whether you invest or not.
At 3% inflation a year:
| After | €100,000 has the purchasing power of |
|---|---|
| 10 years | €74,409 |
| 20 years | €55,368 |
| 30 years | €41,199 |
A hundred thousand euros under your mattress buys less than forty-two thousand euros' worth in thirty years.
This is why every long-term calculation must use real returns: your nominal return divided by inflation, not subtracted from it. The savings-rate table above uses 5% real, which at 2 to 3% inflation means roughly 7 to 8% nominal.
Why the chart always disappoints early on
This is why people quit, and it's purely a matter of shape.
In the first years your accumulated wealth is small, so the return on it is small too. Almost everything you see growing is your own contribution. It feels like saving with extra steps.
For Anna in the example: after ten years of contributing she has put in €36,000 and holds roughly €52,000. Nice, no miracle. The miracle happens in the thirty years that follow, in which that amount grows to €395,270 without her adding another euro.
The crossover point, the day your annual return exceeds your annual contribution, sits for most people somewhere between year ten and year fifteen. Before then you're mostly building conviction. After that it builds itself.
That's also why tracking your wealth matters more in the early years than later. Not because the numbers are impressive, but because a visible line makes it easier to keep going during the phase where there's little to see.
What does this mean for your FIRE number?
Three things follow from the above.
Calculate in real terms, not nominal. Your target sits in today's euros, so your return should too. Use 7% nominal against a target in current euros and you'll think you're finished years before you are.
Your spending is the lever, not your return. Every euro you permanently stop spending lowers your target by twenty-five euros and raises your monthly contribution. Every euro of extra return only does the second.
The final years go fastest. Precisely when you get impatient, the curve accelerates. Anyone ten years out from their target is further along than the running total suggests.
Where does doing it by hand break down?
A compound-interest spreadsheet is quick to build and almost always too optimistic, for three reasons.
It uses one fixed return, while reality consists of good and bad years. That matters: the order of returns affects your outcome as soon as you contribute or withdraw along the way.
It assumes a fixed monthly contribution, while almost nobody contributes the same amount for thirty years.
And it never compares itself to reality. You build the projection once, and never check again whether you're still on it.
How Gylder shows this
Gylder doesn't project a future from an assumed percentage. What it shows is your actual curve: a daily snapshot of your wealth going back as far as your data does, in which compound growth becomes visible as something that genuinely happened rather than something a formula promises.
The bridge calculator also works out your target amount and date. Gylder tracks your progress against it and projects from your own measured growth: not from 7% because that's the historical average. Behind schedule, and it says so. Ahead, likewise.
That's a deliberate choice. A projection built on your own figures has a shorter horizon and is less impressive than a chart running forty years forward, but it's yours.
What this doesn't tell you
Compound interest is mathematics applied to an assumption. The mathematics is always right; the assumption rarely is.
Returns don't arrive evenly. An average of 7% over thirty years can consist of a year at +25% and a year at −18%. For the final amount the order barely matters as long as you withdraw nothing. Withdraw, which is exactly what you do once you reach FIRE, and the order suddenly matters a great deal. A bad first year after you stop weighs more heavily than a bad year ten years later.
Historical returns aren't a promise. Every calculation here uses percentages based on the past. That's the best available and it's no guarantee.
The model doesn't know your life. Job loss, a renovation, a divorce, a child. The formula carries on as though your monthly contribution survives thirty years untouched.
Frequently asked questions
What's the difference between interest and return? Interest is an agreed payment, for instance on a savings account. Return is the outcome of an investment and isn't fixed. The compounding mechanism works identically for both.
How often should interest be added? More often is better, but the difference is small. At 7% a year, monthly compounding over thirty years yields about 5% more than annual. With investing this hardly applies, because prices move continuously.
Does compound interest work on a savings account? Yes, but the return there is usually low enough that inflation eats it. At 2% interest and 3% inflation your balance compounds in euros while your purchasing power falls.
What's a realistic return to calculate with? For a globally diversified equity portfolio, most long-term calculations use 5 to 7% real. Whatever you pick, a single figure covering thirty years is an assumption, not a forecast.
Why doesn't my own home count here? Home equity compounds too, but produces no income while you live in it. For a target calculation it therefore counts differently from an investment portfolio of the same size.