Compound interest: how to grow your savings
Compound interest is, in the phrase often attributed to Einstein, the eighth wonder of the world. The idea is simple — interest that earns interest — but its consequences are counter-intuitive enough that most people underestimate it badly. Here is how it works, with the actual numbers.
Simple vs. compound interest
With simple interest, you earn interest only on the initial capital, so growth is a straight line. With compound interest, each period's interest is added to the capital and earns further interest itself: growth becomes exponential. The difference looks trivial at first and enormous later.
| €10,000 at 5 % a year | Simple interest | Compound interest |
|---|---|---|
| After 10 years | €15,000 | €16,289 |
| After 20 years | €20,000 | €26,533 |
| After 30 years | €25,000 | €43,219 |
In the first decade compounding adds a modest €1,289 over simple interest. By year 30 the gap is over €18,000 — the compound balance is not growing by €500 a year like the simple one, but by more than €2,000 a year, because the interest itself has become capital.
The formula, demystified
For a lump sum, the final amount is FV = C × (1 + r)n, where C is the initial capital, r the rate per period and n the number of periods. Check it against the table: €10,000 × 1.0510 = €16,288.95. For monthly plans, the same logic applies month by month with r = annual rate ÷ 12 — tedious by hand, instant with a compound interest calculator.
One subtlety worth knowing: compounding frequency. A quoted 6 % compounded monthly is really (1 + 0.06/12)12 − 1 ≈ 6.17 % effective per year. That is the difference between the nominal rate (TIN in Spanish bank jargon) and the effective annual rate (TAE). When comparing products, always compare effective rates.
Ana vs. Borja: the cost of waiting ten years
Ana invests €200/month from age 25 to 65 (40 years). Borja invests the same €200/month but starts at 35 (30 years). Both earn 6 % a year, compounded monthly.
- Ana: contributes €96,000 → ends with about €398,000
- Borja: contributes €72,000 → ends with about €201,000
Ana contributed only 33 % more money, but finishes with almost double. The €24,000 she invested in her first decade did more work than everything Borja invested in thirty years of catching up. Time in the market is the one input you cannot buy back later.
How growth accelerates: the same plan over time
The €200/month plan at 6 % is worth tracking decade by decade:
| Years saving | Total contributed | Balance | Growth share |
|---|---|---|---|
| 10 | €24,000 | €32,776 | 27 % |
| 20 | €48,000 | €92,408 | 48 % |
| 30 | €72,000 | €200,903 | 64 % |
| 40 | €96,000 | €398,298 | 76 % |
Notice the pattern: in the first decade, most of the balance is simply your own money. By the fourth decade, three of every four euros are growth. The curve feels flat for years and then appears to explode — it was exponential all along.
The rule of 72
A useful mental shortcut: to estimate how many years your money takes to double, divide 72 by the annual rate. At 6 %, capital doubles roughly every 12 years (the exact figure is 11.9 — the rule is a very good approximation for ordinary rates). At 3 %, doubling takes about 24 years; at 8 %, about 9. The rule also works in reverse, and grimly: at 3 % inflation, the purchasing power of cash halves every 24 years. Money that is not growing is quietly shrinking.
Compounding works against you too
The same mathematics powers debt. A revolving credit card at 20 % doubles what you owe in under four years if unpaid (72 ÷ 20 ≈ 3.6). And small recurring costs compound in reverse: a 1.5 % annual management fee on an investment fund does not cost you 1.5 % — over 30 years it silently consumes a large slice of the final balance, because every euro of fees is a euro that stops compounding for you. This is also why paying down expensive debt is often the best "investment" available, and why the maths of mortgage overpayments mirrors the maths of saving.
How to make compounding work for you
- Start early, even small: as Ana showed, early euros are the most powerful ones you will ever invest.
- Be consistent: automatic monthly contributions remove willpower from the equation and buy through good and bad markets alike.
- Reinvest everything: withdrawing the interest converts compound growth back into simple growth — the top row of our first table instead of the bottom.
- Watch costs and taxes: prefer low fees, and use tax-advantaged wrappers where available, so compounding works on gross returns as long as possible.
- Be patient with the flat years: the spectacular part of the curve only exists for those who stayed through the boring part.
Frequently asked questions
Is 6 % a realistic rate?
It is a common long-run assumption for diversified equity investing, but it is an illustration, not a promise — real returns vary year to year and can be negative. Run your own plan with conservative and optimistic rates to see the range.
Does inflation ruin the calculation?
It reduces real purchasing power, so a useful trick is to compound at an inflation-adjusted rate (for example 6 % nominal − 2 % inflation = ~4 % real). The exponential logic is unchanged.
Lump sum or monthly contributions?
Mathematically, money invested earlier compounds longer, so a lump sum available today generally beats drip-feeding it. Monthly plans win in practice because most people's income arrives monthly — the best plan is the one you sustain.
Project your savings with regular contributions, any rate and any horizon — and see the year-by-year breakdown.
Compound interest calculator →