New words for this lesson
Say them out loud. Then use one word in a sentence.
€10,000 now — or 1 cent doubled?
Option A: €10,000 today. Option B: 1 cent that doubles every day for 30 days.
🤔 Which option ends up bigger?
Show answer
Option B — by a lot. After 30 days the cent has become €5,368,709.12.
Look at the path: day 10 it is only €5.12. Day 20: €5,242.88. Day 25: €167,772.16. Almost all the growth happens at the end.
That is exponential growth. Doubling every day is not real life — but the shape of the curve is.
Interest that makes its own interest
With simple interest you always earn on your starting amount. With compound interest you earn on the starting amount plus everything it has earned so far — as long as you reinvest it instead of taking it out.
🤔 What is the one ingredient compounding needs most?
Show answer
Time. Not a big amount, not a perfect rate — time. The curve only gets steep if you leave it alone long enough.
The compound calculator
Type a starting amount, what you add every month, a yearly rate and the years.
Example numbers only, and a fixed rate every year. Real returns go up and down, and they can be negative. This is not advice — it is maths.
Two savers, one big surprise
Both save €50 a month. We use an example return of 6% per year, and both stop at 65.
| Saver | Pays in | |
|---|---|---|
| 🐠 Ada · saves from 20 to 30, then stops | €6,000 | 10 years |
| 🐢 Ben · saves from 35 to 65 | €18,000 | 30 years |
🤔 Ben pays in three times more money. Who has more at 65?
Show answer
Ada — with about €62,980, while Ben has about €50,230.
Ada paid in €12,000 less. Her money simply had more time to compound. Starting early beats paying in more.
Calculated with 6% per year as an example. Change the rate and the numbers change — but the pattern stays.
Compounding also works against you
Interest on a debt compounds too. Unpaid credit card interest becomes part of the debt — and then earns interest itself.
🤔 So who is compounding working for, when you only pay the minimum on a credit card?
Show answer
For the bank, not for you. Same maths, other direction. Lesson 14 shows what that costs.
Zusatzwissen · extra knowledge
A quick trick: the rule of 72. Divide 72 by the yearly rate and you get roughly the years until money doubles. At 6%: 72 ÷ 6 = about 12 years. It is an estimate, not an exact formula.