Question 1:
Show your working for all calculations. Calculate dollar values to 2 decimal places. Investment A has an interest rate of 8.5% p.a. calculated yearly. An investor has $5,000.
(a) Will Investment A or a simple interest account paying 8.5% p.a. earn more money? Explain.
(b) How much will the Investment A be worth after 4 years?
(c) How long will it take for Investment A to double the initial deposit?
(d) How much interest will accrue after 5 years if the interest at 8.5% p.a. is compounded
(i) 6-monthly? (ii) quarterly? (iii) continuously?
(e) Calculate the APR if interest at 8.5% p.a. is compounded quarterly.
(f) Investment B offers 8.25% compounded weekly. Is this a better investment than Investment A?
Show suitable calculations.
Question 2:
For this question, MATLAB and the spreadsheet may be helpful. If you present working from Excel or MATLAB, what you have done must be clear to the marker.
For each of the following systems of equations,
(i) without solving, what is known about the solution(s)? Explain your answer.
(ii) if there is a unique solution, find it. Show how you obtain your answer.
(iii) If there is a unique solution, verify it (ie, substitute the "x values"). Show your working.
(a) 4x1 + 5x2 + 2x3 + 14x4 = 167.5
3x1 + 9x2 + 4x3 + 21x4 = 263.5
8x1 + 10x2 + 7x3 + 28x4 = 365.0
7.5x1 - x2 - 10x3 + 9x4 = -13.25
15x1 - 2x2 - 20x3 + 18x4 = -26.5
(b) 4x1 + 5x2 + 2x3 + 14x4 = 167.5
3x1 + 9x2 + 6x3 + 21x4 = 283.5
8x1 + 10x2 + 7x3 + 28x4 = 365.0
11x1 - x2 - 10x3 + 9x4 = -11.5
(c) -10x1 + 10x3 + 2x4 - 9x5 = 79.79
-4x1 + 8x2 + 3x3 - 5x4 + 3x5 = 117.87
10x1 - 9x2 + 4x3 + 9x4 - x5 = -76.99
4x1 + 2x2 - 7x3 - 8x4 + 2x5 + x52 = -71.82
-3x1 - 9x2 + 5x3 - 3x4 + 4x5 = -28.94
3x1 + 10x2 - 5x3 + 6x4 + 5x5 = 97.65
Question 3:
Show your working for all calculations. Calculate dollar values to 2 decimal places.
(a) Mary bought a car in September 2006 for $27,000. In 5 years it depreciated to $0.
Is this an example of straight-line or reducing balance depreciation? Explain your answer. For parts (b) - (d), depreciation is by the reducing balance method.
(b) Joe bought a computer for $1,800. If it depreciates at 20% p.a., what will it be worth in 2 years?
(c) Joe will buy a new model when the value of his old computer reaches $750.
How long will this take?
(d) How much longer would Joe keep the old computer if the rate of depreciation were 16%?
Question 4:
Show your working for all calculations. Calculate dollar values to 2 decimal places.
Jim borrowed $175,000 for 5 years at 5.88% per annum, compound interest, payable quarterly.
(a) Construct and display a schedule of payments, showing (in the following order) for each quarter:
• the amount of principal outstanding at the start of each quarter
• the quarterly payment
• the amount paid off the principal in that quarter
• the amount paid off the interest in that quarter
• the amount of principal outstanding at the end of the quarter.
Explain how you calculated each of these 5 components.
(b) On one pair of axes, graph, construct a fully-labelled graph to show, over the term of the loan, the amount paid off the principal in each quarter and the corresponding amount paid off the interest in that quarter.
(c) (i) For this loan, obtain the comparison rate.
(ii) If the loan had an upfront fee of $1,000 and a fee (payable at the end of each year) of $250,
obtain the comparison rate. Express your answer as a percentage to 2 decimal places.
Question 5
Show your working.
Consider the system of equations below.
(b2 - 4)x1 + x3 = b - 2
x3 = 2
x1 + x2 + x3 = 4 where -∞ < b < ∞.
Does this system have
(a) zero solutions?
(b) one solution?
(c) infinitely many solutions?
Explain your answer, by using the rank property of matrices.
Question 6
Show your working for all calculations. Calculate dollar values to 2 decimal places.
Investment scheme A requests an upfront payment of $5,000. For this, it promises successive payments over the next 5 years of $800, $1,000, $1,200, $1,400 and $1,600. The discount rate is 8%.
(a) Calculate the present value of each of the future payments.
(b) Calculate the NPV for investment scheme A. Is this scheme profitable?
(c) Investment scheme B continues scheme A into a sixth year, in which an investor will receive $1,800.
Is investment scheme B profitable?
(d) If the discount rate were 5.5%, would investment scheme A be profitable after 5 years?
(e) For investment scheme A, with discount rate 8%, use Excel's
(i) =NPV function to calculate the NPV, correct to the nearest cent.
(ii) =IRR function to calculate the IRR, as a percentage correct to 4 decimal places.
For your calculations, you MUST display your Excel formulas AND you MUST also display the row and column headings (see the Excel Tips below) so that your formulas can be interpreted.
Attachment:- Q2.xlsx