BEA140 Quantitative Methods Assignment 1 - Semester 2, 2020

(54 marks in total)

Due Date for Assignment Milestones: 4:00pm Friday 7 August 2019

Due Date for Assignment Submission: 4:00pm Friday 14 August 2019

Contribution to Unit Assessment: 9%

Students MUST read the assignment guidelines located at the end of this assignment, and in particular the highlighted section about misconduct.

Question 1: [18 marks]

You are considering investing in a scholarship fund for your daughter. The fund operates in the following way:

• Starting in one month’s time you would make regular monthly deposits of $50 for a period of eight years into a scholarship fund. Immediately after your final deposit the fund would pay $10,000 to your daughter to help her with expenses when she commences university study.

a) Illustrate this scenario as a fully labelled time line diagram.

[2 marks]

To be able to compare this fund with other possible investments, you need to know the effective interest rate, j12, that this fund returns.

b) Derive and present the equation of equivalence that is appropriate for this scenario. Do NOT seek to simplify the expression, but rather leave $10,000 as the value of the left hand side (LHS). [Hint: This is a “Price is Right” problem but with a FV.]

[4 marks]

c) Using an estimate of i=1%, determine the value of the right hand side (RHS) of the equation of equivalence. Enter this value to 2 decimal places as an answer to “Assignment 1 – Milestones” question 1c. You can have as many attempts of this as you wish without penalty, but this question will close at 4:00pm on Friday 7 August. There will be no marks available for this question part after then.

[2 marks]

d) Present you next three estimates of i and the corresponding value of the right hand side of the equation of equivalence. Ensure that for each of these three steps you explain why you increased or decreased the value of i.

[6 marks]

e) Determine a value of i, for which the LHS and RHS of the equation of equivalence vary by no more than $1.00. NB You do not need to show any working for this question part, but merely present your answer, and the values of the RHS and LHS.

[2 marks] f) Thus determine the effective interest rate, j12, that this scholarship returns.

[2 marks]

Question 2 [18 marks]

A retiree deposits $500,000 in a bank account which pay interest j12 = 5.4% p.a.

Starting in a month’s time, they intend to withdraw $4000 to cover their living expenses until run out of money. [NB It is likely that their final withdrawal will be a partial withdrawal].

a) Illustrate this scenario as a fully labelled time line diagram.

[2 marks]

b) Determine how many full sized withdrawals they can mark. Enter this value as an answer to “Assignment 1 – Milestones” question 2b. You can have as many attempts of this as you wish without penalty, but this question will close at 4:00pm on Friday 7 August. There will be no marks available for this question part after then.

[2 marks] c) Determine the size of the final partial withdrawal made one month after the last full sized withdrawal.

[4 marks]

d) Construct an amortization schedule showing the last three withdrawals (two full and one partial withdrawals. Ensure that you show how you found the outstanding principal. Ensure that you have shown example calculations for one line of the table. {NB this scenario is essentially the same as a fully amortized loan repayment, except the person and the institution have swapped roles.)

[4 marks]

e) After exactly one year, they had to have hip replacement surgery, and had to withdraw an extra $15000 from the account to cover the cost. That is, their 12th withdrawal was $19000 rather than the usual $4000. Determine how many more full sized withdrawals they can make after this.

[6 marks]

Question 3: [18 marks]

You wish to save $2000 to go on a holiday when you finish university in 2.5 year’s time. You plan to do this by making regular deposits of the same size into a savings account that pays interest j52 = 4.68% p.a., starting in one week’s time.

a) Illustrate this scenario as a fully labelled time line diagram.

[2 marks]

b) Determine the deposit size required. Enter this value to 2 decimal places as an answer to “Assignment 1 – Milestones” question 3b. You can have as many attempts of this as you wish without penalty, but this question will close at 4:00pm on Friday 7 August. There will be no marks available for this question part after then.

[2 marks] c) Explain and perform a sanity check on your answer to (b)

[1+1=2 marks]

d) Immediately after your 50th deposit, the interest rate increases to j52=4.78 % p.a. Draw an appropriate time line of the scenario and then determine what deposit size will now be needed for deposits 51 to 130 in order to still meet your original target of $2000.

[2+6=8 marks]

e) Determine how much will be accumulated at the end of the savings scheme if you continue with the old weekly deposit size after the interest rate changes.

[4 marks]

RUBRIC : Assessment Guidelines The rubric below provides a guideline for students of the expectations with respect to key assessment criteria.

Criteria Applies To Excellent Intermediate Poor

Assumptionsi Questions or question parts

• Identify and state any assumptions required to allow the use of a particular methodology. • No Penalty • Assumptions identified but misstated or misrepresented. • Penalty 0-1 marks • Failure to identify and state an assumption required to allow the use of a particular methodology, or use of a wrong assumption.

• Penalty 1-2 marks

Methodology • Student shows understanding of the problem.

• Appropriate methodology chosen for the problem.

• Enough detail in the answer for the marker to follow the logic of the student's approach. (As an example, the level of detail provided in examples in lecture notes.)

• Student shows correct formula and/or student shows appropriate Excel function with parameters.

• No Penalty • Student shows some understanding of the problem.

• General approach basically correct, but some steps wrong or inappropriate.

• Marker has some difficulty following student’s approach and/or there are significant jumps of logic or missing details.

• Student refers to but doesn’t show correct formula or students refers to appropriate Excel function without specify parameters.

• Penalty = 50% of marks available. • Student shows no understanding of the problem.

• Totally inappropriate methodology employed.

• Large or incorrect jumps of logic.

• Marker cannot follow student's approach.

• Important details missing.

• Neither correct formula nor appropriate Excel function are referred to.

• Penalty = 50% of marks available

Evaluation • Answers are correct, given the values that the student started the problem (or problem part) with.ii • No penalty. • Minor calculation and/or transcription errors leading to incorrect answers. • Penalty 1 mark. • Major and/or repeated errors. • Penalty 1-2 marks.

Interpretation and reflection • Interpretations, when asked for are correct and complete.

• Answers are feasible. • No penalty • Interpretations, when asked for, are partially correct or partially complete.

• Answer is NOT feasible but the student identifies and explains why the answer can't be right.

• Penalty 1 mark. • Interpretations, when asked for are either well off the mark or are missing.

• Answer is NOT feasible but the student does not identify or explain this. • Penalty 2 marks.

Presentation Whole Assignment

• Submitted as a “.pdf” document, and has cover sheet.

• Meet minimum standards expected of a business professional:

o Pages numbered, questions and question parts assembled in order.

o Prepared as a computer document (NOT a scanned hand written copy) using a clear readable font (9 to 12 point)

o Diagrams/Tables/Charts computer generated, labelled and appearing in correct sequence within an answer, and location clearly identified is this is not possible.iii

o Mathematical expressions and equations presented using an equation editor or using fixed font approach as demonstrated in unit videos.

o Clear use of appropriate language and terminology.

o Final answer to question parts presented in a sentence. For example, “R=427.51” is not an acceptable answer, but “The weekly deposit required is R=$427.51” is acceptable.

o Cover sheet attached and completed.

• No penalty Some of the following failings

• Wrong file format -10%

• Pages not numbered -2%

• Inappropriate font -2%

• Hand written (unless permission obtained beforehand) -10%

• At least one diagram/table/chart unlabelled 1 to 2%

• At least one diagram/table/chart out of sequence (or not referenced if in an appendix) 1 to 2%

• Diagram/table/chart hand written (unless permission obtained beforehand) 1-2%

• At least one expression not appropriately formatted 1 to 2%.

• Language/terminology unclear or inappropriate 1-2%

• Answers not expressed in sentences 1-2%

• Cover sheet missing or incomplete -2%

(Items marked 1-2%, are 1% for single offence, 2% if there is more than one offence). Most of the failings listed in the previous column.

Timeliness • Handed in on or before due date.

• No penalty • As per unit outline • Handed in more than a week late, or not handed in, without prior arrangement and supporting documentation.

• 100% penalty

Guidelines for BEA140 Quantitative Methods Assignment

Teams & Individuals

• The assignment may only be completed and submitted by individuals. Team assignments are not allowed.

• Whereas students are encouraged to discuss all elements of the unit, including the assignment, the preparation of the assignment must be an individual effort. For example, two or more students discussing how to attack question 2, for example, is acceptable. Two students working together to prepare a full solution to question 2 is NOT acceptable. A student presenting others’ work as their own is

NOT acceptable. A student allowing another student to copy all or part of their assignment is NOT acceptable. (See note about plagiarism at bottom of page.)

Presentation

• Assignments must be submitted with a completed cover sheet. If an assignment is submitted without, the assignment and mark will be withheld until the student submits it.

• The assignment should be prepared on a word processor, and submitted as a “.pdf” document. It is imperative that students carefully read the Assessment Guidelines Rubric (previous page). Students are expected to show sufficient working such that the marker can establish the logic of their thoughts. (Typically, the amount of working in examples in the lectures is a good indication of what is an acceptable amount of detail.). Part marks will be available for incorrect answers, and will be allocated on the basis of the working.

• Methodology – additional information: Because markers need to be able to follow the logic and structure of answer, simply providing Excel printouts IS NOT AN ACCEPTABLE METHODOLGY.

Preparation Methodology

• Students are encouraged to check their answers, and ask themselves questions such as -does this make sense?-, -how can I tell if this looks reasonable?- If a student gets an answer that is obviously wrong and can't figure out what has gone wrong, they are expected to at least comment that it does not look reasonable (and why).

• Students are encouraged to complete assignment questions as the relevant topics are covered in class. (The -mad rush at the last minute- strategy is a dangerous one. See Problems below.)

Problems

• Assignments that are handed in late will be penalised, unless prior arrangement has been made with the lecturer. Assignments up to one week late will be penalised as described in the unit outline. Assignments more than one week late will not be marked.

• In the event of sickness or other major disruption is likely to affect a student’s ability to submit the assignment on time, the lecturer should be contacted a.s.a.p. Special consideration will require documentary evidence. (Medical certificate, memo on letterhead for participation in representative (Tas, or Aust) sport or for interstate work commitments, etc…)

• Special consideration will most likely assume that the individual was working on the assignment as recommended in the Preparation Methodology section above. For example, if one is sick for the last week before the assignment is due, it may well be expected that all of the assignment that should have been prepared during previous weeks will be submitted on time, and that only the questions pertaining to the last week's work will be granted an extension.

• If you have any other questions or problems contact your lecturer or tutor - the earlier the better.

Marking and Feedback

• It will take a number of weeks to mark the assignment.

• However, one week after the due date, a full and detailed set of solutions will be posted on mylo. Students are encouraged to keep a copy of their assignment which they can check against the solutions, and thus obtain feedback on their performance even before the assignments are marked. This strategy is designed to allow students to take maximum advantage of the assignment in their exam preparation study.

• Upon return of marked assignments, teaching staff will be available for those students seeking more feedback.

You should be aware that assignments will be checked for academic misconduct. Academic misconduct is punishable by reduction or cancellation of marks, and in the most serious cases, exclusion from a unit, a course or the University. This applies both to a student who submits somebody else’s work as their own, AND to a student who willingly allows another to copy and submit their work. More information is available at https://www.utas.edu.au/students/learning/academic-integrity. Please note, markers are obligated to look for misconduct, and are obligated to report it if they find it.

i NB Sometimes questions may not need students to state any assumption as these may have been provided in the question.

ii If a student makes a mistake on a question part they will lose marks on that question part. If they then use a resulting incorrect number in a subsequent question part, as far as possible they will not penalised in that subsequent part, except where it should have become obvious to the student that an error was carried in.

iii For instance, if a diagram is required as part of an answer to part (b), it should be with the rest of part (b) and between parts (a) and (c). If a diagram is too large to fit into the answer sequence it should be included as an appendix at the end of the document, with a clear reference to it in the answer sequence. E.g. “see appendix 3 for the diagram associated with the answer”.

(54 marks in total)

Due Date for Assignment Milestones: 4:00pm Friday 7 August 2019

Due Date for Assignment Submission: 4:00pm Friday 14 August 2019

Contribution to Unit Assessment: 9%

Students MUST read the assignment guidelines located at the end of this assignment, and in particular the highlighted section about misconduct.

Question 1: [18 marks]

You are considering investing in a scholarship fund for your daughter. The fund operates in the following way:

• Starting in one month’s time you would make regular monthly deposits of $50 for a period of eight years into a scholarship fund. Immediately after your final deposit the fund would pay $10,000 to your daughter to help her with expenses when she commences university study.

a) Illustrate this scenario as a fully labelled time line diagram.

[2 marks]

To be able to compare this fund with other possible investments, you need to know the effective interest rate, j12, that this fund returns.

b) Derive and present the equation of equivalence that is appropriate for this scenario. Do NOT seek to simplify the expression, but rather leave $10,000 as the value of the left hand side (LHS). [Hint: This is a “Price is Right” problem but with a FV.]

[4 marks]

c) Using an estimate of i=1%, determine the value of the right hand side (RHS) of the equation of equivalence. Enter this value to 2 decimal places as an answer to “Assignment 1 – Milestones” question 1c. You can have as many attempts of this as you wish without penalty, but this question will close at 4:00pm on Friday 7 August. There will be no marks available for this question part after then.

[2 marks]

d) Present you next three estimates of i and the corresponding value of the right hand side of the equation of equivalence. Ensure that for each of these three steps you explain why you increased or decreased the value of i.

[6 marks]

e) Determine a value of i, for which the LHS and RHS of the equation of equivalence vary by no more than $1.00. NB You do not need to show any working for this question part, but merely present your answer, and the values of the RHS and LHS.

[2 marks] f) Thus determine the effective interest rate, j12, that this scholarship returns.

[2 marks]

Question 2 [18 marks]

A retiree deposits $500,000 in a bank account which pay interest j12 = 5.4% p.a.

Starting in a month’s time, they intend to withdraw $4000 to cover their living expenses until run out of money. [NB It is likely that their final withdrawal will be a partial withdrawal].

a) Illustrate this scenario as a fully labelled time line diagram.

[2 marks]

b) Determine how many full sized withdrawals they can mark. Enter this value as an answer to “Assignment 1 – Milestones” question 2b. You can have as many attempts of this as you wish without penalty, but this question will close at 4:00pm on Friday 7 August. There will be no marks available for this question part after then.

[2 marks] c) Determine the size of the final partial withdrawal made one month after the last full sized withdrawal.

[4 marks]

d) Construct an amortization schedule showing the last three withdrawals (two full and one partial withdrawals. Ensure that you show how you found the outstanding principal. Ensure that you have shown example calculations for one line of the table. {NB this scenario is essentially the same as a fully amortized loan repayment, except the person and the institution have swapped roles.)

[4 marks]

e) After exactly one year, they had to have hip replacement surgery, and had to withdraw an extra $15000 from the account to cover the cost. That is, their 12th withdrawal was $19000 rather than the usual $4000. Determine how many more full sized withdrawals they can make after this.

[6 marks]

Question 3: [18 marks]

You wish to save $2000 to go on a holiday when you finish university in 2.5 year’s time. You plan to do this by making regular deposits of the same size into a savings account that pays interest j52 = 4.68% p.a., starting in one week’s time.

a) Illustrate this scenario as a fully labelled time line diagram.

[2 marks]

b) Determine the deposit size required. Enter this value to 2 decimal places as an answer to “Assignment 1 – Milestones” question 3b. You can have as many attempts of this as you wish without penalty, but this question will close at 4:00pm on Friday 7 August. There will be no marks available for this question part after then.

[2 marks] c) Explain and perform a sanity check on your answer to (b)

[1+1=2 marks]

d) Immediately after your 50th deposit, the interest rate increases to j52=4.78 % p.a. Draw an appropriate time line of the scenario and then determine what deposit size will now be needed for deposits 51 to 130 in order to still meet your original target of $2000.

[2+6=8 marks]

e) Determine how much will be accumulated at the end of the savings scheme if you continue with the old weekly deposit size after the interest rate changes.

[4 marks]

RUBRIC : Assessment Guidelines The rubric below provides a guideline for students of the expectations with respect to key assessment criteria.

Criteria Applies To Excellent Intermediate Poor

Assumptionsi Questions or question parts

• Identify and state any assumptions required to allow the use of a particular methodology. • No Penalty • Assumptions identified but misstated or misrepresented. • Penalty 0-1 marks • Failure to identify and state an assumption required to allow the use of a particular methodology, or use of a wrong assumption.

• Penalty 1-2 marks

Methodology • Student shows understanding of the problem.

• Appropriate methodology chosen for the problem.

• Enough detail in the answer for the marker to follow the logic of the student's approach. (As an example, the level of detail provided in examples in lecture notes.)

• Student shows correct formula and/or student shows appropriate Excel function with parameters.

• No Penalty • Student shows some understanding of the problem.

• General approach basically correct, but some steps wrong or inappropriate.

• Marker has some difficulty following student’s approach and/or there are significant jumps of logic or missing details.

• Student refers to but doesn’t show correct formula or students refers to appropriate Excel function without specify parameters.

• Penalty = 50% of marks available. • Student shows no understanding of the problem.

• Totally inappropriate methodology employed.

• Large or incorrect jumps of logic.

• Marker cannot follow student's approach.

• Important details missing.

• Neither correct formula nor appropriate Excel function are referred to.

• Penalty = 50% of marks available

Evaluation • Answers are correct, given the values that the student started the problem (or problem part) with.ii • No penalty. • Minor calculation and/or transcription errors leading to incorrect answers. • Penalty 1 mark. • Major and/or repeated errors. • Penalty 1-2 marks.

Interpretation and reflection • Interpretations, when asked for are correct and complete.

• Answers are feasible. • No penalty • Interpretations, when asked for, are partially correct or partially complete.

• Answer is NOT feasible but the student identifies and explains why the answer can't be right.

• Penalty 1 mark. • Interpretations, when asked for are either well off the mark or are missing.

• Answer is NOT feasible but the student does not identify or explain this. • Penalty 2 marks.

Presentation Whole Assignment

• Submitted as a “.pdf” document, and has cover sheet.

• Meet minimum standards expected of a business professional:

o Pages numbered, questions and question parts assembled in order.

o Prepared as a computer document (NOT a scanned hand written copy) using a clear readable font (9 to 12 point)

o Diagrams/Tables/Charts computer generated, labelled and appearing in correct sequence within an answer, and location clearly identified is this is not possible.iii

o Mathematical expressions and equations presented using an equation editor or using fixed font approach as demonstrated in unit videos.

o Clear use of appropriate language and terminology.

o Final answer to question parts presented in a sentence. For example, “R=427.51” is not an acceptable answer, but “The weekly deposit required is R=$427.51” is acceptable.

o Cover sheet attached and completed.

• No penalty Some of the following failings

• Wrong file format -10%

• Pages not numbered -2%

• Inappropriate font -2%

• Hand written (unless permission obtained beforehand) -10%

• At least one diagram/table/chart unlabelled 1 to 2%

• At least one diagram/table/chart out of sequence (or not referenced if in an appendix) 1 to 2%

• Diagram/table/chart hand written (unless permission obtained beforehand) 1-2%

• At least one expression not appropriately formatted 1 to 2%.

• Language/terminology unclear or inappropriate 1-2%

• Answers not expressed in sentences 1-2%

• Cover sheet missing or incomplete -2%

(Items marked 1-2%, are 1% for single offence, 2% if there is more than one offence). Most of the failings listed in the previous column.

Timeliness • Handed in on or before due date.

• No penalty • As per unit outline • Handed in more than a week late, or not handed in, without prior arrangement and supporting documentation.

• 100% penalty

Guidelines for BEA140 Quantitative Methods Assignment

Teams & Individuals

• The assignment may only be completed and submitted by individuals. Team assignments are not allowed.

• Whereas students are encouraged to discuss all elements of the unit, including the assignment, the preparation of the assignment must be an individual effort. For example, two or more students discussing how to attack question 2, for example, is acceptable. Two students working together to prepare a full solution to question 2 is NOT acceptable. A student presenting others’ work as their own is

NOT acceptable. A student allowing another student to copy all or part of their assignment is NOT acceptable. (See note about plagiarism at bottom of page.)

Presentation

• Assignments must be submitted with a completed cover sheet. If an assignment is submitted without, the assignment and mark will be withheld until the student submits it.

• The assignment should be prepared on a word processor, and submitted as a “.pdf” document. It is imperative that students carefully read the Assessment Guidelines Rubric (previous page). Students are expected to show sufficient working such that the marker can establish the logic of their thoughts. (Typically, the amount of working in examples in the lectures is a good indication of what is an acceptable amount of detail.). Part marks will be available for incorrect answers, and will be allocated on the basis of the working.

• Methodology – additional information: Because markers need to be able to follow the logic and structure of answer, simply providing Excel printouts IS NOT AN ACCEPTABLE METHODOLGY.

Preparation Methodology

• Students are encouraged to check their answers, and ask themselves questions such as -does this make sense?-, -how can I tell if this looks reasonable?- If a student gets an answer that is obviously wrong and can't figure out what has gone wrong, they are expected to at least comment that it does not look reasonable (and why).

• Students are encouraged to complete assignment questions as the relevant topics are covered in class. (The -mad rush at the last minute- strategy is a dangerous one. See Problems below.)

Problems

• Assignments that are handed in late will be penalised, unless prior arrangement has been made with the lecturer. Assignments up to one week late will be penalised as described in the unit outline. Assignments more than one week late will not be marked.

• In the event of sickness or other major disruption is likely to affect a student’s ability to submit the assignment on time, the lecturer should be contacted a.s.a.p. Special consideration will require documentary evidence. (Medical certificate, memo on letterhead for participation in representative (Tas, or Aust) sport or for interstate work commitments, etc…)

• Special consideration will most likely assume that the individual was working on the assignment as recommended in the Preparation Methodology section above. For example, if one is sick for the last week before the assignment is due, it may well be expected that all of the assignment that should have been prepared during previous weeks will be submitted on time, and that only the questions pertaining to the last week's work will be granted an extension.

• If you have any other questions or problems contact your lecturer or tutor - the earlier the better.

Marking and Feedback

• It will take a number of weeks to mark the assignment.

• However, one week after the due date, a full and detailed set of solutions will be posted on mylo. Students are encouraged to keep a copy of their assignment which they can check against the solutions, and thus obtain feedback on their performance even before the assignments are marked. This strategy is designed to allow students to take maximum advantage of the assignment in their exam preparation study.

• Upon return of marked assignments, teaching staff will be available for those students seeking more feedback.

You should be aware that assignments will be checked for academic misconduct. Academic misconduct is punishable by reduction or cancellation of marks, and in the most serious cases, exclusion from a unit, a course or the University. This applies both to a student who submits somebody else’s work as their own, AND to a student who willingly allows another to copy and submit their work. More information is available at https://www.utas.edu.au/students/learning/academic-integrity. Please note, markers are obligated to look for misconduct, and are obligated to report it if they find it.

i NB Sometimes questions may not need students to state any assumption as these may have been provided in the question.

ii If a student makes a mistake on a question part they will lose marks on that question part. If they then use a resulting incorrect number in a subsequent question part, as far as possible they will not penalised in that subsequent part, except where it should have become obvious to the student that an error was carried in.

iii For instance, if a diagram is required as part of an answer to part (b), it should be with the rest of part (b) and between parts (a) and (c). If a diagram is too large to fit into the answer sequence it should be included as an appendix at the end of the document, with a clear reference to it in the answer sequence. E.g. “see appendix 3 for the diagram associated with the answer”.

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