Simple to compound

SubjectMathematics YearYear 10 Time225

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Introduction

This set of resources provides opportunities for students to use technology to solve problems involving compound interest in the context of superannuation. Students connect the compound interest formula to repeated applications of simple interest and use the simple interest formula to explore how super grows.

Australian Curriculum or Syllabus

Achievement standard

By the end of Year 10, students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities. They make the connections between algebraic and graphical representations of relations. Students solve surface area and volume problems relating to composite solids. They recognise the relationships between parallel and perpendicular lines. Students apply deductive reasoning to proofs and numerical exercises involving plane shapes. They compare data sets by referring to the shapes of the various data displays. They describe bivariate data where the independent variable is time. Students describe statistical relationships between two continuous variables. They evaluate statistical reports.

Students expand binomial expressions and factorise monic quadratic expressions. They find unknown values after substitution into formulas. They perform the four operations with simple algebraic fractions. Students solve simple quadratic equations and pairs of simultaneous equations. They use triangle and angle properties to prove congruence and similarity. Students use trigonometry to calculate unknown angles in right-angled triangles. Students list outcomes for multi-step chance experiments and assign probabilities for these experiments. They calculate quartiles and inter-quartile ranges.

Content descriptions

Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229).

Teacher resources

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Visualiser

Using spreadsheets

Student learning resources

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Explainer

The magic of compound interest and super

 
Worksheet

Super calculations from simple to compound

 
Investigation

Watch your super grow

Suggested activity sequence

This sequence is intended as a framework to be modified and adapted by teachers to suit the needs of a class group. If you assign this activity to a class, your students will be assigned all student resources on their 'My learning' page. You can also hand-pick the resources students are assigned by selecting individual resources when you add a work item to a class in 'My classes'.

Part A: What is compound interest?

  1. Use a grouping strategy to organise students in groups of 3 or 4.
  2. Students read the explainer and in groups construct a brief definition of superannuation and compound interest. Each group writes their definition on the board.
  3. When all definitions are displayed, discuss the concept of super and compound interest and develop simple class definitions.

Part B: Super calculations from simple to compound

  1. As a class read part 1 of the worksheet.
  2. Use the information table to demonstrate simple interest and compound interest formulas.
  3. Model to students how to use spreadsheets to solve problems. Use the visualiser if necessary. You could also refer students to Making an excel spreadsheet – Flowchart and/or Making an excel spreadsheet – How-to-sheet if needed.
  4. Students complete part 1 of the worksheet.
  5. As a class, read through part 2 of the worksheet and use the information table to explain how repeated applications of simple interest can be used to calculate interest on interest.
  6. Students complete part 2 of the worksheet.
  7. As a class, read through part 3 of the worksheet and discuss the superannuation guarantee. Use the information table to explain the process of adding the super guarantee to the super balance and interest earned.
  8. Students complete part 3 of the worksheet.
  9. As a class, work through the information tables on part 4 of the worksheet and discuss and if necessary, demonstrate the difference between using the compound interest formula to calculate interest annually and monthly.
  10. Students complete part 4 of the worksheet.
  11. Work through student solutions and conclusions for the worksheet with the whole class.

Part C: Growing your super

  1. Walk students through the instructions for each task in the investigation.
  2. Students may benefit from working individually and/or in small discussion groups.
  3. You may choose to group students according to readiness and distribute tasks accordingly. Task 1 is the least challenging and task 2 is the most challenging.
  4. You may wish to use this as an assessment task. If so, negotiate with students what they will submit to you for marking and develop an assessment rubric which includes success criteria. Otherwise, conduct a class discussion to hear student’s findings and ensure all of them have a general understanding of the idea that more frequent payments will improve their super balance.