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Compound interest

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

You put 1000 € in the bank for 3 years at \(5\,\%\). The interest stays in the account. Then the interest also earns interest: compound interest (der Zinseszins).
📄 Open worksheet (PDF, German)

The video

In the video the capital grows year by year. At the end there is a formula with a power.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:19 Interest on interest
  3. 0:47 Year by year
  4. 1:05 The formula
  5. 1:37 Careful, mistake!
  6. 2:00 Try it yourself

The most important points

Year 1: \(1000 \cdot 1{,}05 = 1050\). In year 2 there is interest on 1050 €: \(1050 \cdot 1{,}05 = 1102{,}50\). That is 52,50 € instead of 50 €.

The interest from the first year also earns interest.
The interest from the first year also earns interest.
Every year times 1{,}05: after 3 years 1157,63 €.
Every year times \(1{,}05\): after 3 years 1157,63 €.

The formula

final capital = starting capital · \(q^n\) with the interest factor \(q = 1 + \frac{p}{100}\) and \(n\) years: \(1000 \cdot 1{,}05^3 \approx 1157{,}63\).

After 10 years: 1000 · 1{,}05^{10} \approx 1628{,}89.
After 10 years: \(1000 \cdot 1{,}05^{10} \approx 1628{,}89\).

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
Page 2/3
Show the worksheet solutions
The worksheet – Page 3
Page 3/3

Try it yourself

Task

2000 € are in the bank for 2 years at \(2\,\%\). How much money is it at the end?

Show solution

\(2000 \cdot 1{,}02^2 = 2080{,}80\), so 2080,80 €

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Zinseszins (Zinsfaktor, Kapital Jahr für Jahr, Formel mit Potenz). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.