BEA140 Data Analysis for Business
Assignment
Your assignment must be submitted electronically to MyLo by 4.00 pm (CTC) on November 8th. Please also submit a hard copy of your assignment to the local lecturer, Scott Guoqiang (scott.guoqiang@utas.edu.au).
Read instructions carefully before attempting the assignment.
Instructions
• This assignment must be completed and submitted by each individual student.
• Answer all FIVE (5) questions.
• When any calculations are required, show all the steps you take to reach your answer. No marks will be given if all necessary steps are not shown.
• Answers must be in sentence form. so that single-word or single-number answers without explanation will be considered incomplete.
• Type your answers to each question on A4-sized paper.
• See Lecture 1’s Lecture Notes (pages 32-33) for guidance on how to present equations and formulas.
• On the frontpage, please attach the assignment cover sheet available on MyLo under the Assignments tab.
• Save your file as a PDF named “BEA140_Assignment_123456.pdf”, where
123456 is your student ID. Please do not submit your Excel working file – your answers need to be presented in your PDF file.
Question 1
Suppose you put $7,000 in your saving account and your bank offers an interest rate of 10% per annum. What will be the compounded amount in five years (FV) and the corresponding annual effective rate (AER) if
(a) it is compounded quarterly? [5 marks]
(b) it is compounded monthly? [5 marks]
[Total marks: 10]
Question 2
A loan of $5,000, with a monthly interest rate of 1.5%, is repaid through 60 monthly payments of $100, with the first payment due in one month.
(a) What is the interest rate per annum? [5 marks]
(b) How many years will it take to pay off the loan if the payment is only $80 per month. [5 marks]
(c) Suppose we want to pay off the loan after 4 years. How much do we need to pay each month? [5 marks]
[Total marks: 15]
Question 3
The following is the timeline of a monthly cash flow with an interest rate ofj12 = 6% per annum.
(a) Find the future value of the cash flow if X= Y = $100. [5 marks]
(b) Find the future value of the cash flow if X = 120 and Y = 150. [5 marks]
(c) Suppose the future value of this cash flow is $1,220. Find the size of payment YifX= 80. [5 marks]
[Total marks: 15]
Question 4
Suppose James wants to buy a house in Tasmania and borrows $500,000 from the Commonwealth Bank. The bank offers an interest rate ofj12 = 8% per annum. He agrees to repay this loan with monthly payments over 30 years, with the first payment occurring one month after the loan is taken out.
(a) Determine the amount of the monthly payments. [5 marks]
(b) After making 25 payments James lost his job and missed the 26th, 27th, 28th and 29th payments. By the time of the 30th, the repayment schedule resumed. How much does the 30th payment need to be to return to the original payment schedule? [10 marks]
(c) After making 240 payments, the interest rate decreases to 6% per annum. Determine the new monthly payment required for him to pay off the loan in the original 30-year term as agreed with the bank. [10 marks]
(d) Construct an amortization table that shows the last three payments (i.e., two full payments and a partial payment).[10 marks]
[Total marks: 35]
Question 5
A social scientist aims to analyse the relationship between consumption and income and has collected the following data on the annual income of 10 households and their corresponding annual consumption.
|
Household ID
|
Income
|
Consumption
|
|
1
|
67,640.52
|
56,832.64
|
|
2
|
54,001.57
|
52,472.63
|
|
3
|
59,787.38
|
53,635.09
|
|
4
|
72,408.93
|
60,535.52
|
|
5
|
68,675.58
|
59,159.78
|
|
6
|
40,227.22
|
35,850.15
|
|
7
|
59,500.88
|
57,071.10
|
|
8
|
48,486.43
|
39,763.35
|
|
9
|
48,967.81
|
42,739.59
|
|
10
|
54,105.99
|
41,014.31
|
(a) Determine the Pearson correlation (r) between income and consumption. What do you conclude? [5 marks]
(b) Use the Ordinary Least Squares to find the sample regression equation for the model below:
Income = a + bConsumption + u
[10 marks]
(c) Interpret the estimated coefficients (a and b) in part (b). [5 marks]
(d) Calculate the coefficient of determination. What do you conclude? [5 marks]
[Total marks: 25]