BN101 - imm
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ASSIGNMENT 2ND SEMESTER :
BUSINESS NUMERACY 1 (BN101)
CHAPTERS COVERED
: :
2 AND 5 (Wegner, 2004) 1, 2 AND 4 (Zidel, 2010)
LEARNER GUIDE DUE DATE TOTAL MARKS
: : :
UNITS 1 TO 4 3:00 p.m. 21 AUGUST 2012 100
INSTRUCTIONS TO CANDIDATES FOR COMPLETING AND SUBMITTING ASSIGNMENTS The complete ‘Instructions to Students for Completing and Submitting Assignments’ must be collected from any IMM GSM office, the relevant Student Support Centre or can be downloaded from the IMM GSM website. It is essential that the complete instructions be studied prior to commencing your assignment. The following points highlight only a few important notes. 1. You are required to submit ONE assignment per subject. 2. The assignment will contribute 20% towards the final examination mark, and the other 80% will be contributed by the examination, however, the examination papers will count out of 100%. 3. Although your assignment will contribute towards your final examination mark, you do not have to earn credits for admission to the examinations; you are automatically accepted on registering for the exam. 4. Number all the pages of your assignment (e.g. page 1 of 4) and write your name and surname, student number and subject at the top of each page. 5. The IMM GSM requires assignments to be presented in a typed format, on plain A4 paper. Unless otherwise specified, this assignment must be completed within a limit of 1500 words, excluding the bibliography. Students who exceed the word limit may find that only part of the submitted assignment will be marked. 6. A separate assignment cover, which is provided by the IMM GSM, must be attached to the front of each assignment. 7. Retain a copy of each assignment before submitting, in case the original does not reach the IMM GSM. 8. The assignment due date refers to the day up to which assignments will be accepted for marking purposes. The deadline is 3:00 p.m. on 21 August 2012. Late assignments will be accepted, but 25 marks will be deducted from the maximum mark, if received after 3:00 p.m. on 21 August 2012 and up to 5:00 p.m. the following day, after which no assignments will be accepted. 9. If you fail to follow these instructions carefully, the IMM Graduate School of Marketing cannot accept responsibility for the return of the assignment. It may even result in your assignment not being marked. Results will be available on the IMM GSM website, www.immgsm.ac.za, on Friday, 5 October 2012
Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
Page 2 of 5
Answer ALL the questions
IMPORTANT: You may not give the final answer only to any of the questions. You need to show the interim steps of how you arrived at the answer, as this will also be allocated marks. If the final answer is given without any of your workings, you’ll receive 1 mark for the correct answer only. Please use graph paper where graphs are required. QUESTION 1 1.1
[37]
Your organisation has the option of making an investment in new software that will cost R130 000 today and is estimated to provide the savings shown in the following table over its five year life: Year 1 2 3 4 5
Savings estimate R 35 000 50 000 45 000 25 000 15 000
Should the firm make this investment if it requires a minimum annual return of 9% on all investments? (7) 1.2
You can deposit R10 000 into an account paying 9% per annum either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today? (6)
1.3
An insurance agent is trying to sell you an annuity, which for a single amount paid today will provide you with R12 000 at the end of each year for the next 25 years. You currently earn 9% on other investments comparable to the annuity. What is the most you would pay for this annuity? (3)
1.4
Manuel wishes to determine how long it will take an initial deposit of R10 000 to double if he earns 10% per annum on the deposit. (3)
1.5
Tim is shopping for a used car. He has found one priced at R45 000. The dealer told Tim that if he can come up with a deposit of R5 000, the dealer will finance the balance of the price at 12% per annum over two years (24 months). Assuming that Tim accepts the dealers offer, what will his monthly (end-of-month) payment be? (3)
Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
Page 3 of 5
1.6
You invest R3 000 per annum at the end of each year for 3 years at 10% per annum. You then withdraw R2 000 from the account and the balance is invested for another four years. How much will you have in the account at the beginning of the 5th year? (5)
1.7
JD Traders wishes to borrow R200 000. FirstBank offers a rate of 8.5% for one year. Interest is payable in advance. SecondBank offers a rate of 8.9% with interest payable at maturity. ThirdBank offers a rate of 8.2% per annum payable half-yearly, at maturity. What is the effective rate of interest to JD Traders under each option? At which Bank should JD Traders place the loan? (10)
QUESTION 2 2.1
2.2
2.3
[29]
Suppose you randomly selected 10 house prices in the Gauteng area. You are interested in the typical house price. Prices listed to R100 000 (R’000) were: 2.7, 2.9, 3.1, 3.4, 3.7, 4.1, 4.3, 4.7, 4.7, 40.8 (a)
Calculate the mean and median house price.
(4)
(b)
Indicate which of the two measures you will use as an indication of the average house price in Gauteng and give your reason(s). (2)
Suppose a group of 10 students achieved the following scores in a test: 60, 72, 64, 67, 70, 68, 71, 68, 73, 59. Calculate the following for the data set of scores: (a) The first quartile
(2)
(b)
The third quartile
(2)
(c)
The quartile range
(1)
(d)
The standard deviation
(3)
Below is the data for a group of students. Calculate the following for the weight (kg) of the students from the dataset below: (a)
Mean
(2)
(b)
Median
(2)
(c)
Standard deviation
(3)
(d)
Construct a frequency distribution
(3)
(e)
Draw a histogram
(5)
Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
Page 4 of 5
First Height Weight Name (cm) (kg) Aaron 176 66 Alan 182 61 Alastair 173 72 Amelia 167 48 Andrew 193 40 Andrew 177 55 Peter 170 65 Antony 188 80 Belinda 179 58 Campbell 183 79 Catherine 169 60 Charles 178 65 Charlotte 163 87 Colin 175 63 Pierre 178 93 David 180 72 Sean 185 82 Doug 188 82 Emma 169 70 Fiona 158 59 QUESTION 3
[14]
3.1
Complete the following table by writing your answers next to the corresponding letters A – N in your script: (e.g. P = R4 500) Selling Price VAT Selling Price Cost Price % mark-up (exc. VAT) (14%) (incl. VAT) R2 000 20% on cost A B C R2 000 20% on selling price D E F G 25% on cost R3 000 H I J 40% on cost K L R9 576 R4 500 25% on selling price M R840 N (½ mark for each correct answer = 14 x ½ = 7)
3.2
Complete the following table by writing your answers next to the corresponding letters A – N in your script: (e.g. P = R4 500)
Number of units sold 1000 C 1200 K
Cost price per unit R50 R150 G R210
Total Cost R50 000 R75 000 R96 000 R168 000
% mark-up on cost price A D H 12
% mark-up on selling price B E 6.54 L
Mark-up R5.00 R22.50 I M
Selling Price R55.00 F R85.60 N
Total Sales R55 000.00 R86 250.00 J R188 160.00
(½ mark for each correct answer = 14 x ½ = 7) Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
Page 5 of 5
QUESTION 4
[20]
4.1
What is a linear function?
4.2
By completing the table of values below, plot the following linear functions on the same axes: (8) (a)
f(x) = 2x+ 1
(b)
f(x) = 3x−2
(c)
f(x) = 4−3x
(d)
f(x) = 2–x
x
-2
-1
(2)
0
1
2
2x+ 1 3x−2 4−3x 2–x 4.3
Find the gradient and the vertical intercept for each of the following linear functions: 2y +4x = 12 (2) 5x – y = 9
(2)
-3x = 1 – 4y
(2)
4.4
Write down two different functions in which all the graphs are represented by parallel lines. (2)
4.5
Write down two different functions in which all the graphs have the same vertical intercept. (2)
ASSIGNMENT TOTAL: 100
Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
ASSIGNMENT 2ND SEMESTER :
BUSINESS NUMERACY 1 (BN101)
CHAPTERS COVERED
: :
2 AND 5 (Wegner, 2004) 1, 2 AND 4 (Zidel, 2010)
LEARNER GUIDE DUE DATE TOTAL MARKS
: : :
UNITS 1 TO 4 3:00 p.m. 21 AUGUST 2012 100
INSTRUCTIONS TO CANDIDATES FOR COMPLETING AND SUBMITTING ASSIGNMENTS The complete ‘Instructions to Students for Completing and Submitting Assignments’ must be collected from any IMM GSM office, the relevant Student Support Centre or can be downloaded from the IMM GSM website. It is essential that the complete instructions be studied prior to commencing your assignment. The following points highlight only a few important notes. 1. You are required to submit ONE assignment per subject. 2. The assignment will contribute 20% towards the final examination mark, and the other 80% will be contributed by the examination, however, the examination papers will count out of 100%. 3. Although your assignment will contribute towards your final examination mark, you do not have to earn credits for admission to the examinations; you are automatically accepted on registering for the exam. 4. Number all the pages of your assignment (e.g. page 1 of 4) and write your name and surname, student number and subject at the top of each page. 5. The IMM GSM requires assignments to be presented in a typed format, on plain A4 paper. Unless otherwise specified, this assignment must be completed within a limit of 1500 words, excluding the bibliography. Students who exceed the word limit may find that only part of the submitted assignment will be marked. 6. A separate assignment cover, which is provided by the IMM GSM, must be attached to the front of each assignment. 7. Retain a copy of each assignment before submitting, in case the original does not reach the IMM GSM. 8. The assignment due date refers to the day up to which assignments will be accepted for marking purposes. The deadline is 3:00 p.m. on 21 August 2012. Late assignments will be accepted, but 25 marks will be deducted from the maximum mark, if received after 3:00 p.m. on 21 August 2012 and up to 5:00 p.m. the following day, after which no assignments will be accepted. 9. If you fail to follow these instructions carefully, the IMM Graduate School of Marketing cannot accept responsibility for the return of the assignment. It may even result in your assignment not being marked. Results will be available on the IMM GSM website, www.immgsm.ac.za, on Friday, 5 October 2012
Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
Page 2 of 5
Answer ALL the questions
IMPORTANT: You may not give the final answer only to any of the questions. You need to show the interim steps of how you arrived at the answer, as this will also be allocated marks. If the final answer is given without any of your workings, you’ll receive 1 mark for the correct answer only. Please use graph paper where graphs are required. QUESTION 1 1.1
[37]
Your organisation has the option of making an investment in new software that will cost R130 000 today and is estimated to provide the savings shown in the following table over its five year life: Year 1 2 3 4 5
Savings estimate R 35 000 50 000 45 000 25 000 15 000
Should the firm make this investment if it requires a minimum annual return of 9% on all investments? (7) 1.2
You can deposit R10 000 into an account paying 9% per annum either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today? (6)
1.3
An insurance agent is trying to sell you an annuity, which for a single amount paid today will provide you with R12 000 at the end of each year for the next 25 years. You currently earn 9% on other investments comparable to the annuity. What is the most you would pay for this annuity? (3)
1.4
Manuel wishes to determine how long it will take an initial deposit of R10 000 to double if he earns 10% per annum on the deposit. (3)
1.5
Tim is shopping for a used car. He has found one priced at R45 000. The dealer told Tim that if he can come up with a deposit of R5 000, the dealer will finance the balance of the price at 12% per annum over two years (24 months). Assuming that Tim accepts the dealers offer, what will his monthly (end-of-month) payment be? (3)
Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
Page 3 of 5
1.6
You invest R3 000 per annum at the end of each year for 3 years at 10% per annum. You then withdraw R2 000 from the account and the balance is invested for another four years. How much will you have in the account at the beginning of the 5th year? (5)
1.7
JD Traders wishes to borrow R200 000. FirstBank offers a rate of 8.5% for one year. Interest is payable in advance. SecondBank offers a rate of 8.9% with interest payable at maturity. ThirdBank offers a rate of 8.2% per annum payable half-yearly, at maturity. What is the effective rate of interest to JD Traders under each option? At which Bank should JD Traders place the loan? (10)
QUESTION 2 2.1
2.2
2.3
[29]
Suppose you randomly selected 10 house prices in the Gauteng area. You are interested in the typical house price. Prices listed to R100 000 (R’000) were: 2.7, 2.9, 3.1, 3.4, 3.7, 4.1, 4.3, 4.7, 4.7, 40.8 (a)
Calculate the mean and median house price.
(4)
(b)
Indicate which of the two measures you will use as an indication of the average house price in Gauteng and give your reason(s). (2)
Suppose a group of 10 students achieved the following scores in a test: 60, 72, 64, 67, 70, 68, 71, 68, 73, 59. Calculate the following for the data set of scores: (a) The first quartile
(2)
(b)
The third quartile
(2)
(c)
The quartile range
(1)
(d)
The standard deviation
(3)
Below is the data for a group of students. Calculate the following for the weight (kg) of the students from the dataset below: (a)
Mean
(2)
(b)
Median
(2)
(c)
Standard deviation
(3)
(d)
Construct a frequency distribution
(3)
(e)
Draw a histogram
(5)
Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
Page 4 of 5
First Height Weight Name (cm) (kg) Aaron 176 66 Alan 182 61 Alastair 173 72 Amelia 167 48 Andrew 193 40 Andrew 177 55 Peter 170 65 Antony 188 80 Belinda 179 58 Campbell 183 79 Catherine 169 60 Charles 178 65 Charlotte 163 87 Colin 175 63 Pierre 178 93 David 180 72 Sean 185 82 Doug 188 82 Emma 169 70 Fiona 158 59 QUESTION 3
[14]
3.1
Complete the following table by writing your answers next to the corresponding letters A – N in your script: (e.g. P = R4 500) Selling Price VAT Selling Price Cost Price % mark-up (exc. VAT) (14%) (incl. VAT) R2 000 20% on cost A B C R2 000 20% on selling price D E F G 25% on cost R3 000 H I J 40% on cost K L R9 576 R4 500 25% on selling price M R840 N (½ mark for each correct answer = 14 x ½ = 7)
3.2
Complete the following table by writing your answers next to the corresponding letters A – N in your script: (e.g. P = R4 500)
Number of units sold 1000 C 1200 K
Cost price per unit R50 R150 G R210
Total Cost R50 000 R75 000 R96 000 R168 000
% mark-up on cost price A D H 12
% mark-up on selling price B E 6.54 L
Mark-up R5.00 R22.50 I M
Selling Price R55.00 F R85.60 N
Total Sales R55 000.00 R86 250.00 J R188 160.00
(½ mark for each correct answer = 14 x ½ = 7) Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
Page 5 of 5
QUESTION 4
[20]
4.1
What is a linear function?
4.2
By completing the table of values below, plot the following linear functions on the same axes: (8) (a)
f(x) = 2x+ 1
(b)
f(x) = 3x−2
(c)
f(x) = 4−3x
(d)
f(x) = 2–x
x
-2
-1
(2)
0
1
2
2x+ 1 3x−2 4−3x 2–x 4.3
Find the gradient and the vertical intercept for each of the following linear functions: 2y +4x = 12 (2) 5x – y = 9
(2)
-3x = 1 – 4y
(2)
4.4
Write down two different functions in which all the graphs are represented by parallel lines. (2)
4.5
Write down two different functions in which all the graphs have the same vertical intercept. (2)
ASSIGNMENT TOTAL: 100
Assignment: 2ndSemester 2012
© IMM Graduate School of Marketing BN101
