QUANTITATIVE METHODS FOR BUSINESS
MATH1053
Assignment 1: Due Thursday April 03, 2025
Question 1: Time Value of Money 34 Marks
a) Use examples to explain/answer the following questions:
i. What is an interest rate. [2 marks]
ii. What is/are the difference(s) between a yearly interest rate and a monthly interest rate? [2 marks]
iii. Why must a given interest rate (e.g., 12% p.a.) be converted to 1% per month when the question states that interest is compounded monthly? [2 marks]
iv. What is/are difference(s) between annuity and compounding interest [4 marks]
Use EXCEL to answer the following questions
b) Jasmine has been offered a 5-year fixed-term account earning 7.20% per annum, compounded quarterly. If she deposits $100,000, calculate the total amount and the interest earned after 5 years. [5 marks]
c) Jack has just started a new job as a property manager and aims to have a $1 million lump sum upon retirement in 15 years. A local bank offers an account with an average interest rate of 6% p.a., compounded weekly. What amount must he deposit at the end of each week to reach his goal? How much interest he could earn? [5 marks]
d) Josh borrowed $45,000 from a local bank. The bank charges Cajun 5.89 % p.a. monthly and requires monthly repayments. For the first year, Jack can only pay interest on the amount he borrowed. After this, he will make repayments including principal and interest.
i. Calculate the monthly repayment that Josh would have to make starting in year two if the entire loan term is 8 years. [4 marks]
ii. Calculate the total interest paid on the loan. [2 marks]
iii. Use EXCEL to set up an Amortisation Schedule for the loan. You only need to include the first two years in your document. For full marks, show the calculations for “i” and “n” in adjacent cells (you can type these). Label each heading in Row 6 with your initials e.g.
“Period-SZ”. [6 marks]
iv. Calculate the outstanding balance for him after three years. [2 marks]
Question 2: Break-even Graphing 15 Marks
Harris has just arrived in Australia as a new university student and is looking for an internet service provider that suits his needs. He has shortlisted two service providers, iNet and NetExp. Both providers charge a fixed monthly fee, which includes a certain amount of data. Additional data usage will incur extra charges based on the amount used. To compare the options, he created the following linear diagram, as shown in Fig. 1.
Fig. 1 The costs for two internet service providers based on data usage per month.
The coordinates for the points are:
A (0,38), B (60,38), C (0,60), D (50,60), and E (140, 78)
a) Explain the meaning of the point E. [2 marks]
b) Calculate the fixed monthly fee for iNet. [2 marks]
c) Determine which provider Harris should use if he needs a minimum of 300GB of data per month using calculations [4 marks]
d) Reproduce the graph using EXCEL. Your graph is required to have the following:
• title of the graph with your ID number as part of the title. [2 marks]
• horizontal and vertical axis titles. [2 marks]
• the point that the costs are equal. [1 mark]
• the region where NetExp is a better option and the region where iNet is a better option. [2 marks]
George has a rose garden with more than 1000 plants. Every early spring, these plants require at least 32kg of nitrogen, 40kg of phosphate, and 48kg of potassium. Additionally, the total amount of nitrogen should not be over 40kg since high nitrogens will lead to fewer flowers on rose bushes.
There are three different produces in the market he can choose from. Rose Superfood is $36 per bag, Sudden Impact on Rose is $30 per bag, and Flower Quick is $32 per bag. The amount of these three primary nutrients from each product is listed in the Table 1 below.
Formulate a mathematical model for this problem. In doing so, consider the following:
a) Define the decision variables for this problem [3 marks]
b) What is the objective for this problem? Using your decision variables, formulate the objective function. [2 marks]
c) What are the constraints in this problem? Using your decision variables, formulate these constraints. [6 marks]
Formulate an Excel worksheet for this problem. In doing so, consider the following:
d) Include the base Excel table with formulas, explanations, solver parameters, and the Answer
Report and Sensitivity Report [6 marks] Using the Excel reports answer the following:
e) What is the optimal solution and the minimum cost for him? [2 marks]
f) Which constraints are not fully met, and by how much? [2 marks]
g) Explain the impact on the optimal solution if the cost of a bag of Rose Superfood increases to $45? [2 marks]
h) Calculate and discuss the new cost if the minimum required phosphate decreases to 39kg. [2 marks]
Question 4: Sampling 16 marks
You are required to download the files from the website: Flow-MER Fish Age | Datasets | data.gov.au - beta for this question. Use the Flow-MER Fish Age 2014-2023(CSV-GEO-AU) to answer the question and refer to the Metadata description for Flow-MER Fish Age 2014-2023(PDF) for data details.
a) Generate a sample dataset containing 10 samples from the CSV file using the simple random sampling method. Explain, step-by-step, how this sample dataset is produced. [3 marks]. Find the average total length for this sample if possible. If not, explain why. [1 mark].
b) Generate a sample dataset containing 10 samples using ‘bias’ sample method. Explain, step-by-step, how this sample dataset is produced. [6 marks].
c) Find the average fork length for all ‘ Nematalosa erebi’ fish listed in the data set if you can. [2 marks]. Discuss if you can use this result to approximate the true population mean for ADULT ‘Nematalosa erebi’ fish. [4 marks]