Annuities
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Introduction
These resources provide students with the opportunity to apply their knowledge and skills relating to compound interest and annuities to a superannuation context to investigate the impact of additional contributions to a super account.
General mathematics
Unit 4
Topic 2: Loans, investments and annuities
Compound interest loans and investments:
- use a recurrence relation to model a compound interest loan or investment, and investigate (numerically or graphically) the effect of the interest rate and the number of compounding periods on the future value of the loan or investment (ACMGM094)
- with the aid of a calculator or computer-based financial software, solve problems involving compound interest loans or investments; for example, determining the future value of a loan, the number of compounding periods for an investment to exceed a given value, the interest rate needed for an investment to exceed a given value. (ACMGM096).
Annuities and perpetuities (compound interest investments with periodic payments made from the investment):
- use a recurrence relation to model an annuity, and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity (ACMGM099).
- with the aid of a financial calculator or computer-based financial software, solve problems involving annuities (including perpetuities as a special case); for example, determining the amount to be invested in an annuity to provide a regular monthly income of a certain amount. (ACMGM100).
Teacher resources
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Annuities - Teachers Notes
Using spreadsheets
Student learning resources
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Annuities
Annuities Spreadsheet
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'.
This investigation is an application of compound interest and annuities in the context of superannuation. It is assumed that students will have the knowledge and skills to perform the calculations – the activity does not support students to learn this as a new skill. The teacher notes may provide you with additional insight. Aside from the resources listed above, you will also need calculators and/or computers with spreadsheet software for each student.
- Walk the students through the instructions for the investigation. They will need to download the annuities spreadsheet to complete the task. If you choose not to use spreadsheets for this investigation, setting up a table to summarise the events and the calculations is an important step in the investigation – it helps clarify for students the sequence of events and provides some structure for their comparisons and conclusions. If necessary, use the visualiser to support students to use spreadsheets.
- Once students have completed the task, as a class, discuss students’ findings.