# Super saver

SubjectMathematics YearSenior secondary Curriculum Time245 ## Introduction

This set of resources provides opportunities for students to solve problems involving percentages, rates and proportions using technology (spreadsheets) in the context of superannuation. The concept of compound interest is introduced through iterative calculations using spreadsheets.

Australian Curriculum or Syllabus

General mathematics

Unit 1

Topic 1: Consumer arithmetic

Applications of rates and percentages:

• apply percentage increase or decrease in various contexts; for example, determining the impact of inflation on costs and wages over time, calculating percentage mark-ups and discounts, calculating GST, calculating profit or loss in absolute and percentage terms, and calculating simple and compound interest (ACMGM006)

• use a spreadsheet to display examples of the above computations when multiple or repeated computations are required; for example, preparing a wage-sheet displaying the weekly earnings of workers in a fast food store where hours of employment and hourly rates of pay may differ, preparing a budget, or investigating the potential cost of owning and operating a car over a year. (ACMGM009)

Unit 3

• use geometric sequences to model and analyse (numerically, or graphically only) practical problems involving geometric growth and decay; for example, analysing a compound interest loan or investment … (ACMGM074).

Essential mathematics

Unit 4

Topic 3: Loans and compound interest

Compound interest:

• review the principles of simple interest (ACMEM168)
• understand the concept of compound interest as a recurrence relation (ACMEM169)
• se technology to calculate the future value of a compound interest loan or investment and the total interest paid or earned (ACMEM171)
• use technology to investigate the effect of the interest rate and the number of compounding periods on the future value of a loan or investment. (ACMEM173)

## Student learning resources

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Explainer

Worksheet

How to

Investigation

## 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: Defining superannuation

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

Part B: Calculating super contributions

1. Explicitly teach students how to calculate super guarantee using a gradual release of responsibility model. An example of modelling is provided below.

You’re a third-year apprentice plumber and your weekly wage is \$669.53 per week. How much super should your employer pay into your super account? Super = 9.5% x salary = 0.095 x 669.53 =\$63.61

2. Give students 5 simple calculations and a sixth one which is a bit more challenging – perhaps a ‘working backwards’ question, for example, if your employer pays \$72.30 into your super account, what’s your salary? Part C: Calculating return on investment for super accounts 1. Discuss investment returns earned on super accounts with students and the comparisons with interest. Consider the amounts people will accumulate in super if they just make contributions. Introduce the idea of interest adding to super balance. 2. Apply the compound interest formula to some super balances to calculate return earned. The main formula for calculating the new balance for compounding interest is: A=P(1+r)n where A=new balance P=original balance (Principal) r=annual interest rate (%) n=time in years Interest I=A-P 3. Do a couple of examples on the board, for example.: Super balance \$52,460, rate 6.5% 2 years.

New balance
P= 52,460
r= 0.065
n= 2
A= P(1+r)n
= 52,460 (1.065)2
=\$59,501.44 Interest I= A-P = \$59,501 - \$52,460 = \$7,041.44

Part D: Practising

1. As a class, talk through the requirements of the worksheetMaking an Excel spreadsheet – Flowchart may be helpful for students.
2. Students complete the worksheet.
3. Work through solutions with the whole class.

Part E: Investigating super

1. Walk the students through the instructions for each task in the investigation.
2. Students complete their investigations.
3. As a class, discuss students’ findings.