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Lesson sheet · Module 7

Interest, compounding, capitalisation

The aim of the lesson

Time multiplies everything — both savings and debts. Before you sign, work out the final amount, not just the percentage and the instalment.

  • 👧 Child: "How much will I have at the end?"
  • 🧑 Teenager: before a loan or "buy now, pay later" — how much do I pay back in total?
  • 🧔 Adult: compare the effective annual rate and the APR. If a promised return doubles the money faster than the rule of 72 allows, with no clear source — run.

Your step in Pecuvo: in "Goals", look at the savings curve. In "Debt" — how much interest is left. Do the sum once, before you sign.

The topic (chapters of the module)

  1. Chapter 1 · Simple interest
  2. Chapter 2 · Compound interest (compounding)
  3. Chapter 3 · Capitalisation: how often interest is added
  4. Chapter 4 · The rule of 72
  5. Chapter 5 · Saving every month: the power of time
  6. Chapter 6 · Inside a loan: the annuity and the APR
  7. Chapter 7 · The real interest rate: nominal minus inflation
  8. Chapter 8 · Today's euro and tomorrow's euro
  9. Chapter 9 · The mathematics of scams

For the youngest · ages 6–7

🐣 The youngest: If you keep your coins for a long time, sometimes more are added to them. This adding is called interest. Then the new coins bring new ones too. Like a snowball that rolls and grows. The longer it rolls, the bigger it gets.

Play together (5 minutes): Put 2 buttons in a bowl. Every day add one new button for every two buttons in the bowl. Count together for 5 days: 2, 3, 4, 6, 9, 13 — the bowl grows faster and faster.

A question for the evening: "What would you wait a long time for, so that it becomes more?"

A game from the catalogue: LV-01 "The tree of patience" — https://pecuvo.eu/igri/katalog/#lv-01 (in Bulgarian)

Questions for the class — 3 per level

  • 👧 1. What is the difference between simple and compound interest? 2. Why is it good to start saving early? 3. What will you ask if someone promises "double every week"?
  • 🧑 1. How much does €1,000 become at 5 % for 10 years? 2. What does the rule of 72 say at 9 %? 3. Why can a loan with a lower instalment be more expensive?
  • 🧔 1. Why do we compare the effective rate and not the nominal one? 2. What is the real interest rate at 2 % nominal and 3 % inflation? 3. Why is "2 % a day" mathematically impossible to sustain?

A 45-minute plan

5 min
The question for the evening or one from “Check yourself” — what do the pupils think? No right or wrong answers.
15 min
One or two chapters of the module at the level of the class (the “child · teenager · adult” buttons on the page).
10 min
The game or the calculator for the topic — in pairs or on the board.
10 min
The questions for the class. If you like, the open test — everyone writes down only their code.
5 min
The iron principle in the pupils' own words and one small step for home.

Tools for the lesson

No personal data of pupils. Children under 14 — with a teacher or a parent. Do not compare individual pupils. Knowledge, not financial advice.

The sheets may be freely printed and copied for lessons, clubs and families, with the source pecuvo.eu. They may not be sold.