Simple to compound
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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.
Achievement standard
By the end of Year 10, students recognise the effect of approximations of real numbers in repeated calculations. They use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying linear, quadratic and exponential functions as appropriate, and solve related equations, numerically and graphically. Students make and test conjectures involving functions and relations using digital tools. They solve problems involving simultaneous linear equations and linear inequalities in 2 variables graphically and justify solutions.
Students interpret and use logarithmic scales representing small or large quantities or change in applied contexts. They solve measurement problems involving surface area and volume of composite objects. Students apply Pythagoras’ theorem and trigonometry to solve practical problems involving right-angled triangles. They identify the impact of measurement errors on the accuracy of results. Students use mathematical modelling to solve practical problems involving proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings. They use deductive reasoning, theorems and algorithms to solve spatial problems. Students interpret networks used to represent practical situations and describe connectedness.
They plan and conduct statistical investigations involving bivariate data. Students represent the distribution of data involving 2 variables, using tables and scatter plots, and comment on possible association. They analyse inferences and conclusions in the media, noting potential sources of bias. Students compare the distribution of continuous numerical data, using various displays, and discuss distributions in terms of centre, spread, shape and outliers. They apply conditional probability to solve problems involving compound events. Students design and conduct simulations involving conditional probability, using digital tools.
Content descriptions
Use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings (AC9M10A04)
Teacher resources
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Using spreadsheets
Student learning resources
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The magic of compound interest and super
Super calculations from simple to compound
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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: Compound interest and super
- Use a grouping strategy to organise students in groups of 3 or 4.
- Students read the explainer and in groups construct a brief definition of superannuation, the super guarantee and compound interest. Each group writes their definition on the board.
- When all definitions are displayed, discuss the concept of super, the super guarantee and compound interest and develop simple class definitions.
Part B: Super calculations from simple to compound
- As a class read part 1 of the worksheet and use the information table to explain how repeated applications of simple interest can be used to calculate interest on interest.
- 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 – How-to-sheet if needed.
- Students complete part 1 of the worksheet.
- As a class, read through part 2 of the worksheet.
- Use the information table to demonstrate simple interest and compound interest formulas.
- Students complete part 2 of the worksheet.
- 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.
- Students complete part 3 of the worksheet.