Introduction to Financial Maths

Overview

This lesson introduces simple and compound interest through everyday financial contexts, building understanding of how interest rate, time, and compounding affect loan and investment growth. It links practical decisions (loans, savings, budgeting) to mathematical models.

Learning intentions

Students will be able to:

• distinguish simple interest from compound interest in realistic scenarios
• calculate total amount and interest for simple and compound interest problems (with clear identification of the formula)
• interpret how changing the interest rate or number of compounding periods affects the result
• communicate reasoning with correct financial maths notation (principal, rate, time, amount)

Success criteria

• I can explain (in my own words) the difference between simple and compound interest.
• I can set up and calculate the total amount and interest for simple and compound interest questions.
• I can state what happens to the final amount when the interest rate increases or compounding periods increase.
• I can show correct substitution and units (e.g., per year, per compounding period).

Curriculum links

• QCAA General Mathematics Unit 4 Topic 1: Loans, investments and annuities 1 — solve practical problems involving compound interest, including determining total amount, total interest, principal, and interest rate per year/per compounding period, and explaining the effect of interest rate and number of compounding periods.
• QCAA Essential Mathematics Unit 4 Topic 3: Loans and compound interest — understand and use compound interest relationships for future value and investigate the effect of principal, interest rate and number of compounding periods on future value.
• QCAA Essential Mathematics Unit 4 Topic 3 — compare, numerically and graphically, the growth of simple and compound interest (as an introduction to later deeper investigations).

Lesson structure (60 minutes)

1. 0–5 min · Hook (real-life finance). Teacher shows a short scenario card: “You save $1,000 in an account: one option earns interest that does not build, another builds each period.” Students quick-write which sounds more like “compound” and why (1–2 sentences).

2. 5–15 min · Direct teach: key ideas and vocabulary. Teacher models the difference using a whiteboard table: principal (P), rate (i), time/periods (n), and amount (A), with clear examples of “interest on original only” vs “interest on current balance.” Students take notes on definitions and complete a “match the description” mini-task (simple vs compound).

3. 15–25 min · Simple interest calculation practice. Teacher works through one guided example step-by-step (choose numbers that fit Year 11 mental estimation):

• Use a simple interest form to find total interest and total amount. Students then do a second similar problem individually, with teacher circulating to check setup, substitution, and final rounding.

4. 25–40 min · Compound interest calculation practice. Teacher introduces the compound interest growth idea: interest is added each compounding period, so future interest applies to a larger base. Teacher demonstrates calculating amount for compounding with a worked example using a future value form (students should see how P, i, n connect to A). Students complete two tasks:

• one guided-then-released calculation (show steps)
• one “identify the parts” task: underline P, circle i, and label n from the question statement.

5. 40–50 min · Compare models: which grows faster? Teacher pairs students and shows two calculations (simple vs compound) on the same starting principal and rate, same number of periods. Students create a 2-row comparison table: Simple vs Compound values and the difference (compound minus simple). Teacher prompts: “What pattern do you notice as periods increase?”

6. 50–57 min · Practical application: budgeting/decision statement. Teacher gives a realistic prompt: “You can either take a loan with simple interest or a savings plan earning compound interest. Which option benefits you more over the same time?” Students write a short decision justification using the computed results and one sentence about the effect of compounding.

7. 57–60 min · Exit ticket (quick check). Students answer two questions:

• “State one correct difference between simple and compound interest.”
• “Given P = 800, rate = 5% per period, n = 3, which is larger: the simple amount or the compound amount? Explain in one sentence.” (They do not need full calculations for the exit ticket question if time is limited; reasoning is required.)

Resources

• Scenario cards (loans and savings options)
• Worked example worksheets (simple and compound templates with spaces for P, i, n, A)
• Student calculators (or digital calculator apps)
• Whiteboard/table for teacher demonstration
• One-page comparison table printable
• Exit ticket slips

Assessment

• Formative checks: teacher observation during guided/independent calculations (correct formula selection and substitution)
• Formative checks: review of the “identify the parts” task (P, i, n correctly extracted)
• Summative-in-miniature: exit ticket reasoning and explanation of simple vs compound

Differentiation

• Support: provide a formula card and step templates (P, i, n → interest → amount); include sentence starters for explanations (“Compound interest gives a larger amount because…”).
• Support for language: allow students to respond with diagrams/tables first, then add one sentence for justification.
• Extension (for students who finish early within the single student class): ask “What happens if the interest rate halves? Predict then verify with one calculation.”
• SEN/EAL considerations: use consistent terminology and highlight keywords in questions (principal, rate, per period, compounding).

Extension (optional)

• SKIP (not requested)