Money and Interest Start

Overview

In this fifth lesson of the “Mastering Year 11 Mathematics” unit, students are introduced to financial mathematics through budgeting, loans, and the difference between simple and compound interest. They will practise choosing the correct interest model and interpreting results in realistic contexts.

Learning intentions

Students will:

• explain what principal, interest rate, and time (number of periods/years) mean in loan and investment situations
• distinguish between simple interest and compound interest using examples
• use the compound interest formula for annual periods to calculate a future value
• interpret results to make a decision about borrowing or saving (at a basic level)

Success criteria

I can:

• identify whether a situation is simple interest or compound interest and justify why
• substitute values correctly into the compound interest formula and calculate the future value accurately
• state what the number I calculated means (e.g., “total amount after … years”)
• compare two options using their calculated totals and recommend the better one based on the context

Curriculum links

• Essential Mathematics Unit 4 Topic 3: Loans and compound interest — understand simple interest variables and identify interest concepts in contexts
• Essential Mathematics Unit 4 Topic 3: calculate future value of a compound interest loan/investment using ( A = P(1+i)^n ) where (i) is interest rate per annum and (n) is number of years
• Essential Mathematics Unit 4 Topic 3: investigate how principal, interest rate, and number of compounding periods affect future value (using guided discussion today)
• Mathematical reasoning and problem-solving in financial contexts: selecting models, substituting into formulas, and interpreting results

Lesson structure (60 minutes)

1. 0–5 min · Hook (real-life starter). Teacher shows a simple scenario: “You borrow $1000 to buy a phone. You repay after 3 years with interest.” Students do a quick think: what costs extra—time, interest rate, or both?
2. 5–15 min · Direct teach: vocabulary and models. Teacher explains principal, interest, interest rate per year, and time in years/periods, then demonstrates simple vs compound with two short numeric examples on the board. Students copy a comparison table (simple: interest on original principal; compound: interest adds each year).
3. 15–28 min · Guided practice: choosing the right model. Teacher gives three mini-cases (e.g., savings account compounding annually, payday-style loan with compound interest language, and a case that is clearly simple). Students work in pairs to label “simple” or “compound” and justify in one sentence using the comparison table. Teacher checks answers and corrects misconceptions.
4. 28–42 min · Worked example: compound interest calculation. Teacher models a full calculation step-by-step for annual compounding:

• Example: “Principal (P=$800), interest rate (i=5%) per annum, for (n=4) years. Find future value (A).” Teacher emphasises converting 5% to 0.05 and using (A=P(1+i)^n). Students complete a second example together, calling out each substitution and exponent value while teacher prompts checks (units and meaning).

5. 42–52 min · Independent task: interpret and decide. Students receive a short two-option task:

• Option 1: Borrowing from A (compound interest)
• Option 2: Borrowing from B (different rate or shorter time) Students calculate the totals for both options (using the same formula structure) and write a recommendation in context: which option costs less or earns more and why. Teacher circulates and targets error patterns (percentage conversion, incorrect power, mixing up total vs interest).

6. 52–58 min · Formative check: “Explain your maths” micro-discussion. Each student shares one step they found tricky and one check they used (e.g., “my total should be bigger than principal when interest is positive”). Teacher records common errors for follow-up.
7. 58–60 min · Exit ticket (quick). Students answer: “A deposit of $500 earns 6% per annum compounded annually for 2 years. Calculate the future value and state what it means in words.”

Resources

• Teacher-made comparison table: simple vs compound interest
• 2–3 sets of mini-case cards for model selection
• Compound interest worked-example slide/board plan (no students copying required beyond key steps)
• Student task sheet with two borrowing/saving options and calculation lines
• Exit ticket paper or digital form (no links)
• Calculator access for each student (ensure same capability expectations)

Assessment

• During guided practice, teacher observes justification quality for choosing simple vs compound interest
• During worked and independent calculations, teacher checks correct substitution, percentage-to-decimal conversion, and correct use of the power (n)
• Exit ticket: verify procedural accuracy (future value) and conceptual interpretation (what the number represents)

Differentiation

• Support: provide a formula “substitution frame” on the student sheet (P, i as decimal, n) and sentence starters for justifications (“This is compound because…”; “The future value means…”).
• Support: allow a calculator workflow check (students must state the decimal form of the rate before evaluating).
• Challenge: require an extra sentence comparing sensitivity: “If the interest rate increased, would the total increase more or less? How do you know from the formula?”
• EAL/SEN: offer model answers for the comparison table entries and encourage “units-first” reasoning (dollars, years, percent per annum) to reduce confusion.