Mathematical ApplicationsInvestment and Loans

Shares

Angela Phillips –Westminster School

Mathematical Applications Stage 2Internal 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)

Investment and LoansExamined TopicInternal 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)

Investment and LoansExamined 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

• 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 LoansExamined Topic – The External Assessment

• 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 LoansExamined Topic – The External Assessment

• 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 LoansExamined Topic – Skills and Application Tasks

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 LoansExamined Topic – Skills and Application Tasks

• 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 LoansExamined Topic – Skills and Application Tasks

Reference: 3

Investment and LoansExamined Topic –Skills and Application Tasks

Reference: 1

Investment and LoansExamined 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.

Reference: 1

Investment and LoansExamined 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.

Reference: 1

Investment and LoansExamined 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.

Reference: 1

Investment and LoansExamined 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.

Reference: 4

Investment and LoansExamined 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.

Reference: 4

Investment and LoansExamined 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.

Investment and LoansExamined Topic – Folio• What is your take away from this session that will

help you teach Investment and Loans this year?

Mathematical Applications Stage 2Internal 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)

SharesNon-Examined TopicInternal 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

Reference: 3

SharesNon-Examined Topic –Skills and Application Tasks

SharesNon-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?

SharesNon-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?

Reference: 4

SharesNon-Examined Topic – Folio

• Please see the handout.

SharesNon-Examined Topic

What is your take away from this session that will help you teach Shares this year?

References

1) Chief Assessor’s reports 2015

2) Exam Paper

3) Subject advice and strategies

4) Sample Folio Tasks

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