This assignment comprises 10% of the assessment for ETF2700 and 10% for ETF5970.
You must submit a printed “hard copy” of your written work - with an Assignment Cover Sheet (from the “Assignments” tab on Moodle).  Submit it in your tutorial before the due time, or submit it to your tutor’s mailbox, 5^th floor H Block, by the due time.
·      A maximum penalty of 20% of the total mark allocated to this assessment will be deducted for each working day that it is late.
·      Extensions beyond the due date will only be allowed in special circumstances.  Contact your tutor.
·      Do not submit your assignment in a folder – stapled pages are easier for the marker.
·      Save trees!  Double-sided printing is encouraged.
·      Retain your marked assignment work until after the publication of final results for this unit.
 
Plagiarism
Intentional plagiarism amounts to cheating in terms of Monash University Statute 4.1 – Discipline.
Plagiarism: Plagiarism means to take and use another person’s ideas and or manner of expressing them and to pass these off as one’s own by failing to give appropriate acknowledgement.  This includes material from any source, staff, students or the Internet – published and unpublished works.
Collusion: Collusion is unauthorised collaboration with another person or persons.
Where there are reasonable grounds for believing that intentional plagiarism or collusion has occurred, this
will be reported to the Chief Examiner, who may disallow the work concerned by prohibiting assessment or
refer the matter to the Faculty Manager.
 
 

 
Question 1    Show your working.
(a)   A and B are non-singular n × n matrices.  Prove that (AB)^-1 = B^-1A^-1.

(b)   We wish to determine the inverse of matrix M without using any electronic calculation device. Obtain, and solve algebraically by elimination, a set of simultaneous equations ·         for a, b and c. ·         for d, e and f. ·         for g, h and i.

M =   M-1 =

 
 
Question 2    Show your working.  (You may use screenshots.)
If you use software in this question, you must use only Excel.
Refer to Worksheet Q2 of Assgt 3.xlsx on Moodle.  For a system of equations, AX = C, in 5 unknowns (x1, x2, x3, x4 and x5), A is the coefficient matrix and C is the right-hand side vector. 
(a)   Obtain the rank of the coefficient matrix.
(b)   Obtain the rank of the augmented matrix.
(c)   From what has been established so far in this question, what is known about this system of equations? 
(No calculation required.)
(d)   Is there a unique solution to this system of equations?  If so, obtain it.  If not, explain why not.
(e)   Is this system of equations ill-conditioned?  Discuss. 
Provide suitable calculations to support your answer.
 
 
Question 3    Show your working, including the formula(s) that you used.  Do not use software.
A rocket travelled 0.5 km in its first minute of flight.  Each minute thereafter, the distance travelled was 40% more than the distance travelled in the previous minute.
(a)        Calculate, correct to 2 decimal places, the distance (km) travelled in the 10^th minute of flight.  
(b)       How long does it take for the rocket to travel a total distance of more than 1,044 km?
Give your answer correct to the nearest minute.
 
 
Question 4    Show your working, including the formula(s) that you used. 
Sharon bought a new car for $24,500.  She has monthly repayments of $937.50 on a flat rate loan for 3 years.
(a)        Calculate the annual flat rate of interest.  Give your answer as a percentage, correct to 3 decimal place.
(b)   A loan of $50,000 has a 9.95% per annum flat rate and monthly payments of $1,456.25 for 4 years.
       (i)    For a flat rate loan, the annual effective rate of interest r is often approximated by the formula
       r = 2nR/(n + 1).  Use this formula to calculate r as a percentage to 3 decimal places.
(ii)        Calculate the annual effective rate of interest, as a percentage, correct to 3 decimal places.   
(iii)       Calculate the nominal rate of interest, as a percentage, correct to 3 decimal places.

 
Question 5    Show your working, including the formula(s) that you used. 

This item appeared recently in Money magazine. For the following calculations, you may ignore taxation and inflation.  Calculate percentages to 3 decimal places. (a)   Assuming that money compounds annually, calculate the percentage discount rate underlying this statement (to which 1/3 of readers agreed). (b)   Assuming that money compounds monthly, calculate the discount rate underlying this statement (to which 1/3 of readers agreed) as (i)      a percentage per month. (ii)     a nominal rate. (iii)    an effective annual rate.

Source: Money/The Beddoes Institute.

(c) ZNA Bank plans to advertise to encourage people to deposit into its new E-friendly account.  The
account pays monthly compounding interest.  Should ZNA advertise the nominal rate or the effective annual rate for the account?  Briefly discuss this
(i)      from the bank’s perspective.
(ii)     from an investor’s perspective.
 
 
Question 6    Show your working.
The mining company OreFull Mining Pty Ltd is considering three alternative investments, each involving an initial outlay of $100 million and yielding a return at the end of each of the next 15 years.  Net returns ($ million) are estimated as shown below.  OreFull has unlimited borrowing capacity on the capital market at a cost of 16% per annum.
Investment A:       $30m per year for the next 15 years.
Investment B:       $20m per year for the next 10 years; $10m per year thereafter.
Investment C:       $20m, $60m and $100m, respectively, for years 1, 2 and 3; $5m per year thereafter.
(a)   For each investment, calculate
(i)      the sum of the returns ($m)
(ii)     the NPV ($m to 3 decimal places).
(iii)    the IRR (as a percentage to 3 decimal places).
(b)   Imagine that you had perused the set of cash flows for each investment before calculation of any NPV
or IRR values.  Were there any indications that C would have the highest IRR?  Briefly give reasons for your answer.
(c)   Without further calculation, how do you know that the NPV for investment B will be negative if the
cost of capital is 21%?
(d)   Explain why the sum of the returns is, or is not, a good criterion on which to compare investments A, B
and C.
(e)   Which of the three investments (give reasons) would you recommend on the basis of
(i)      NPV
(ii)     IRR
(iii)    all things being considered?  Briefly discuss.
Excel TipsETF2700/ETF5970 – MATHEMATICS FOR BUSINESS代写
If you need help with Excel,
·      use Excel’s Help/Microsoft Excel Help menu item.
·      see the “EXCEL” icon on the Moodle site for some Help files.
To display the formulas which underlie your spreadsheet calculations
While pressing the Ctrl key, press the  key.  (You may now need to widen some columns of the spreadsheet in order to fully display the revealed formulas.)
Repeat these key strokes to return to the usual display.
To alter the page margins, in order to optimise the use of a page before printing it
Click on the Office Button and select Print/Print Preview/Preview/ShowMargins.  Then, click on and drag the margins.
To print in “Landscape”           view, rather than in “Portrait”  view
Click on Page Layout (at the top of the screen)/Orientation/Landscape.
To print the gridlines which border the spreadsheet cells
Select Click on Page Layout (at the top of the screen) /Sheet Options/Gridlines/Print
To print the Row (“1”, “2”, “3”, etc) and Column (“A”, “B”, “C”, etc) headings
Before printing, select Click on Page Layout (at the top of the screen) /Sheet Options/Headings/Print
To Copy part of your spreadsheet, eg to Paste it into a Word document
·         Select the desired cells in Excel.
·         Click on the Copy command. 
·         Go to the Word document and select the triangle under the Paste command and select
Paste Special/Picture(Enhanced Metafile).
An alternative to the procedures above is to use “Snipping Tool” when your spreadsheet is displayed.  This captures an image of your screen, which may then be Pasted into a Word document.  Use Word’s “Crop” tool to reduce the Pasted image to your desired selection.
If you are unable to make Excel display the row and column headings clearly on your printout, then you MUST write them on by hand.
 
Word Tips
To capture a screen image & Paste it into Word
To capture the image (any image, eg, an Excel page, an internet page, a photo, etc) currently displayed on your screen,
·         press the Print Scrn button on your keyboard.
·         go to the required location in your Word document.  Hold the Ctrl key and press the letter “V”.
·         to trim (“Crop”) this image, select View/Toolbars/Picture and click on the “Crop” icon:
Then, apply the “Crop” icon to the small square “handles”  of the image.
The “Snipping Tool” (available via START button/Programs/Accessories) is very useful too.
 
To arrange graphs and pictures within a “Word” document
Graphs and pictures can be more manageable if you insert a table into Word and place your graphs and pictures (and text) into cells of the table.
 ETF2700/ETF5970 – MATHEMATICS FOR BUSINESS代写