Compound interest is one of those financial concepts that gets explained either with calculus or with breathless enthusiasm — both unhelpful. The intuition is plain: today's interest earns interest tomorrow. That's the entire idea. Everything else is bookkeeping.
What's actually happening
Imagine you put €1,000 in an account that pays 5% a year. After one year you have €1,050. The next year, the 5% applies not just to your original €1,000 but to the full €1,050. So you earn €52.50 of interest, not €50. The third year, you earn 5% of €1,102.50 — and so on. Each year, the base on which interest is paid is bigger than the year before.
It looks small at first. Over short periods, compound interest is barely distinguishable from simple interest. The whole point is that it accelerates over time, so the difference is invisible early and dominant late.
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Why time matters more than rate
This is the part most articles get backwards. Newer savers focus on chasing a higher rate. Experienced savers focus on starting earlier and continuing longer. Why? Because compounding rewards duration, not heroics.
| Strategy | Annual rate | Years | Final |
|---|---|---|---|
| Save €100/month | 4% | 10 | €14,725 |
| Save €100/month | 4% | 30 | €69,405 |
| Save €100/month | 6% | 10 | €16,388 |
The 30-year, 4% saver ends up with more than four times the money of the 10-year, 6% saver — even though their rate is lower. Time wins.
The Rule of 72
If you ever need a quick mental calculation: divide 72 by your annual rate; the result is how many years it takes for the money to double. So at 6%, money doubles every 12 years. At 4%, every 18. At 2%, every 36. This works perfectly well for any rate between roughly 1% and 12% and saves you reaching for a calculator.
Compounding is the patient cousin of speculation. It is also more reliable.
Where it appears in real life
Compound interest is the engine behind retirement accounts, long-term index funds and — in reverse — credit-card debt. Credit-card balances compound at 18-25%. Left alone, a balance doubles every three or four years. That's why even small debts grow surprisingly fast, and why paying them off is mathematically equivalent to investing at that same rate. Often a better deal than any market opportunity you'll find.
Once you've internalised the idea, you stop chasing rate and start protecting time. That's the whole education.