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](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 - [The whole module on the website](https://pecuvo.eu/en/modules/interest-compounding-capitalisation/) pecuvo.eu/en/modules/interest-compounding-capitalisation/ - [Calculator: Loan and APR](https://pecuvo.eu/en/calculators/loan-repayment-apr/) pecuvo.eu/en/calculators/loan-repayment-apr/ - [Calculator: Compound interest](https://pecuvo.eu/en/calculators/compound-interest/) pecuvo.eu/en/calculators/compound-interest/ - [Calculator: Inflation](https://pecuvo.eu/en/calculators/inflation/) pecuvo.eu/en/calculators/inflation/ - [The open test (9 questions) — pupils write down only their code (e.g. K4B11), no names; the class distribution is shown on the same page](https://pecuvo.eu/en/test/) pecuvo.eu/en/test/ - [The Glossary — terms explained simply](https://pecuvo.eu/en/glossary/) pecuvo.eu/en/glossary/ 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.