This document provides guidance for teachers on teaching the Mathematical Applications topics of Investment and Loans and Shares. For Investment and Loans, an examined topic, it summarizes common student errors on past exams and recommendations for skills and application tasks and folio assessments. For Shares, a non-examined topic, it includes example skills tasks and a sample folio on minimizing interest paid on a home loan. The document concludes by asking teachers to identify their key learnings to apply in teaching these topics.

1. Mathematical
Applications
Investment and Loans
Shares
Angela Phillips –Westminster School

2. Mathematical Applications
Stage 2
Internal Assessments
• Skills and Application Tasks 30% (6 tasks, no part
A’s and B’s)
• Folio 40% (3 tasks, two from the unexamined
topics)
External Assessment
• Examination 30% (from the two chosen examined
topics)

3. Investment and Loans
Examined Topic
Internal Assessments
• Skills and Application Task (only 1, can not be split
into part A and part B)
• Folio (You can chose to do 1 folio for either of your
examined topics)
External Assessment
• Examination (there are two parts to the paper and
this will be one of the parts)

4. Investment and Loans
Examined Topic – The External Assessment
• Simple interest and interest earned on an investment, or interest
paid on a loan, were often confused. Students frequently used
the incorrect formula.
• For the interest-only loan, students miscalculated the interest
payment by calculating it as a compounding loan, or they
calculated the interest paid for the entire year or entire loan.
• The sinking fund as a concept was often confused with the actual
loan. Students failed to show understanding that the sinking
fund is an investment account and hence will grow in value.
More interest being earned in the sinking fund in the second
year was not clearly related to an increased principal.
• The graphics calculator was better used to calculate annuity-type
questions, but some students did not correctly identify the type
of annuity (Pv or Fv) and frequently struggled to correctly apply
negative calculator inputs when n or i were being found.
Reference: 1

5. • The conversion of comparison rates for loans continues to
challenge students. The conversion package on the graphics
calculator should only be applied to compound interest
investments. When students use the effective rates function
on their calculators for loan conversions, it does not factor
in additional monthly fees and charges.
• Some students also completed conversion calculations for
Loan A. The students therefore did not understand that a
loan rate does not change if there are no fees.
• Some students failed to identify that the lower comparison
rate demonstrated which loan was cheaper and should
therefore be used to select the cheaper-costing loan.
Reference: 1
Investment and Loans
Examined Topic – The External Assessment

6. • Students generally could state an assumption in Question
4(f), but were often unable to discuss the effect of this
assumption.
• When there was already money present in the
superannuation fund, students struggled with accurately
calculating the future value.
Reference: 1 and 2
Investment and Loans
Examined Topic – The External Assessment

7. • In general, teachers are offering the appropriate number of
skills and applications tasks (SATs) by setting four SATs from
the two non-examined topics (two tasks per topic) and two
further SATs from the two examined topics (one task per
topic). There are some teachers, however, who continue to
use ‘Part A’ and ‘Part B’ SATs in the examined topics, which
is no longer acceptable. The six specified SATs do not have
to cover all key ideas in the four topics, particularly the
examined topics, where only one SAT is specified.
Preparation for the examination can be undertaken by
offering students appropriate formative tasks which model
the style and coverage of examination questions from
throughout the examined topics. Reference: 1
Investment and Loans
Examined Topic – Skills and Application Tasks

8. Some teachers chose to focus on a specific area of a topic in a
folio investigation and not assess this area in the SATs; for
example, queuing in the Mathematics and Small Business
topic or correlation in the Statistics and Working with Data
topic. This practice is entirely appropriate, provided that the
teacher ensures students are well prepared for questions in
areas not assessed in SATs in the examined topics.
Reference: 1
Investment and Loans
Examined Topic – Skills and Application Tasks

9. • A well-designed SAT contains questions with a good balance of routine and
complex problems to allow for discrimination between students of different
abilities. The mark scheme should also reflect this balance. Teachers are
encouraged to use past examination papers as a guide to the standard
required for SATs. However, these examination questions must not be used
for assessment without significant alteration that renders them
unrecognisable from the source material, as the solutions are in the public
domain.
• Teachers who included the appropriate balance of routine, complex, and
interpretative questions in their SATs gave their students the best chance of
achieving to all grade levels, including the highest level of the performance
standards. In this case, if an appropriate mark scheme was used, the marks
gained on the SATs tended to be a reliable guide to the grade level of the
student’s achievement. It should be noted that if one or more SATs are of a
purely routine nature, then a simple average of the SAT results could result in
an inflated indication of the grade when measured against the performance
standards.
• Teachers should note that excessive scaffolding of questions, such as
providing all the steps or labelling the answer spaces in a question, lowers
the complexity, as it restricts the students’ ability to demonstrate what they
know. Reference: 1
Investment and Loans
Examined Topic – Skills and Application Tasks

10. Reference: 3
Investment and Loans
Examined Topic –Skills and Application Tasks

11. Reference: 1
Investment and Loans
Examined Topic – Folio
• Folio investigations which are too structured or
scaffolded do not provide students with the scope to
demonstrate their own skills and understanding in the
topic. A good investigation provides enough instruction
for students to get started on the investigation, but
leaves options open for them to use initiative and
creativity when carrying out the investigation. In this
way there is support for students who may be
challenged by the investigation, but openness to give
students scope to achieve at the higher grades. If the
first folio investigation requires a little more scaffolding
to support inexperienced students, it is vital that the
other two investigations do not continue to give that
support, so that students have scope to demonstrate
the criteria for the higher grades in the performance
standards.

12. Reference: 1
Investment and Loans
Examined Topic – Folio
• Teachers are advised that in folio investigation
responses students should use current tax rates for
financial calculations and the metric system (not
imperial) for spatial measurements. If calculations
are only shown in appendices, those appendices
must be submitted for moderation as part of the
investigation response. If graphs use a coloured key,
the graphs should be printed in colour when
presented for moderation.

13. Reference: 1
Investment and Loans
Examined Topic – Folio
• Many teachers are marking their work well and
providing excellent feedback to students about their
strengths and weaknesses in the folio investigations.
Students are being encouraged to be succinct in their
presentation of reports and to not fall into the trap of
thinking that a large number of pages of work is
indicative of high quality. Marking the mathematical
calculations within the investigations for correctness is
a necessity for the moderation of student materials
and supports the process of confirming a teacher’s
grade. This marking is also important as a tool for
assisting students to identify where they are applying
skills correctly, and showing them those skills that they
need to review.

14. Reference: 1
Investment and Loans
Examined Topic – Folio
• One area in which many students struggled in their
folio investigations was in addressing the analysis,
assumptions, limitations, and reasonableness of
their results within the context of the problem
being investigated. Often, students in their analysis
would simply recount their results, rather than
discussing the significance and meaning of the
results and then extending this to the possible
impact of the underlying assumptions made in the
mathematical models. In this specific feature of the
performance standards, there was a tendency by
some teachers to award higher grades to
somewhat superficial responses from students.

15. Reference: 4
Investment and Loans
Examined Topic – Folio
Interest Minimisation on a Loan
Introduction
Josh and Emma have just taken out a loan to purchase their new home. They have borrowed
$XXXX (discuss this amount with your teacher), at a current variable rate. The finance officer
suggested they agree to pay the loan back over 25 years as the required repayments will be a
comfortable commitment for them. Josh and Emma agreed with this suggestion, but are keen to
investigate ways of reducing the term and therefore the interest paid on this loan.
Mathematical Investigations
Your task is to demonstrate the effectiveness of a variety of strategies aimed at reducing the term
of the loan and hence the interest paid. You may wish to consider the effect of:
• increasing the size of the regular payment
• any lump sum payments and the timing of these
• changing the timing of the regular payments
• any other strategies.
Analysis/Discussion
Use your mathematical results to critically analyse the outcome of each of the individual scenarios
that you have investigated. Your discussion should include reference to the reasonableness of the
outcome for each scenario and any assumptions made or limitations of the model in this
investigation that could influence your results.
Conclusion
Draw on the analysis of your mathematical results to determine the most appropriate strategy for
Josh and Emma to minimise the interest paid on their loan.

16. Reference: 4
Investment and Loans
Examined Topic – Folio
Interest Minimisation on a Loan
Introduction
Josh and Emma have just taken out a loan to purchase their new home. They have borrowed
$XXXX (discuss this amount with your teacher), at a current variable rate. The finance officer
suggested they agree to pay the loan back over 25 years as the required repayments will be a
comfortable commitment for them. Josh and Emma agreed with this suggestion, but are keen to
investigate ways of reducing the term and therefore the interest paid on this loan.
Mathematical Investigations
Your task is to demonstrate the effectiveness of a variety of strategies aimed at reducing the term
of the loan and hence the interest paid. You may wish to consider the effect of:
• increasing the size of the regular payment
• any lump sum payments and the timing of these
• changing the timing of the regular payments
• any other strategies.
Analysis/Discussion
Use your mathematical results to critically analyse the outcome of each of the individual scenarios
that you have investigated. Your discussion should include reference to the reasonableness of the
outcome for each scenario and any assumptions made or limitations of the model in this
investigation that could influence your results.
Conclusion
Draw on the analysis of your mathematical results to determine the most appropriate strategy for
Josh and Emma to minimise the interest paid on their loan.

17. Investment and Loans
Examined Topic – Folio
• What is your take away from this session that will
help you teach Investment and Loans this year?

18. Mathematical Applications
Stage 2
Internal Assessments
• Skills and Application Tasks 30% (6 tasks, no part
A’s and B’s)
• Folio 40% (3 tasks, two from the unexamined
topics)
External Assessment
• Examination 30% (from the two chosen examined
topics)

19. Shares
Non-Examined Topic
Internal Assessments
• Skills and Application Task (two tasks must be
completed)
• Folio (a folio must be completed for all non-
examined topic)
External Assessment
• Examination There is no externally examined
component for this topic

20. Reference: 3
Shares
Non-Examined Topic –Skills and Application Tasks

21. Shares
Non-Examined Topic –Skills and Application Tasks
• Sam has decided to purchase 1200 shares in CSL
Ltd at their close price of $87.35, with 2%
brokerage and 10% GST. He is concerned about
making a loss if he decided to sell his shares. What
is the breakeven price he would need to sell his
shares for to avoid making a loss?

22. Shares
Non-Examined Topic –Skills and Application Tasks
• Toby bought 1500 shares in Telstra on 14th March
2014 for $13.05 and wants to sell. He has
negotiated brokerage to buy and sell his shares at
1.5%, with 10% GST. His marginal tax rate is 45%.
He can sell his shares on January 17th 2015 for
$14.98 or keep them until the 15th of March when
the price is expected to be $14.02. Toby is keen to
make as much ‘after tax’ profit as he can. If he has
held on to them to sell on March 15th, has he made
the right choice?

23. Reference: 4
Shares
Non-Examined Topic – Folio
• Please see the handout.

24. Shares
Non-Examined Topic
What is your take away from this session that will
help you teach Shares this year?

25. References
1) Chief Assessor’s reports 2015
2) Exam Paper
3) Subject advice and strategies
4) Sample Folio Tasks
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