Simple versus compound interest
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Introduction
This set of resources provides opportunities for students to explore the difference between simple and compound interest. Students construct and compare linear and exponential models, interpret expressions for functions in terms of the situation they model and solve problems.
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
Recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate. (AC9M10A03)
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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Representing linear and exponential growth
Linear and exponential functions card sets
Student learning resources
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Simple versus compound interest
Growing your money
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.
Part A: What is the difference between simple and compound interest?
- Use a grouping strategy to organise students in groups of 3 or 4.
- Students read the explainer and in groups construct a brief description of the difference between simple and compound interest and why it matters.
- As a class, discuss student responses.
Part B: Representing linear and exponential growth
- Display the visualiser and work through each slide, giving students time to answer the questions. The visualiser provides answers to questions you can work through with students if needed.
- Organise students into groups of 3 or 4. Give groups the following linear and exponential function cards in the order given below. Only give them a set of cards after they have matched the previous set.
Card set Groups: 1. Investment plans and formulas Match plans to formulas and develop missing formulas 2. Graphs and tables Complete missing information in tables and match tables with graphs.
Match these with plans and formulas.
3. Statements Match statements with plans, formulas, graphs and tables. - Pair 2 groups to compare and explain their matching.
- Individual groups finalise their matching and create a poster by pasting their matching cards into 2 categories – simple interest and compound interest. Encourage students to provide a rationale for the way they have matched their cards.
- Display completed posters on the wall and allow students to view the work of other groups. If necessary, identify any misconceptions or errors.
- Students complete the worksheet individually.