§ The required savings (6%) represent the percentage
§ And the weekly saving amount is 6% of £600 = £36
Question Three
Base salary = £1000 each month
Commission rate = 5%
Sales = £5640
Total commission is 5% of sales, which is
= 5% of £5640
= £282
Therefore,
Gross earnings = base salary + total commission
= £1000 + £282
= £1282
Question Four
Find the future value and compound interest for a 4-year £7,000 investment that earns 8% compounded monthly.
Principal (P) is £7,000
Interest rate (r) is 8% per annum compounded monthly
Duration (t) is 4 years (48 months)
The future value of the investment (A) is given by the formula below;
Inserting the values above, we get;
A = £9629
Therefore, the future value of the investment is £9629 after 4 years.
Question Five
The principal loan is £6,000
The interest rate is 5.5% per annum
Maturity is 3 years
Assuming simple interest payment, the value of the loan after three years is given as follows;
Total interest accrued = 5.5% of £6,000
= £330
Total loan = principal loan + interest accrued
= £1000 + £330
= £1,330
Task 3: (LO 2 " 3)
Question One
Explain two factors that can contribute to cost recovery of the money paid by PSG.
The two major factors that are likely to contribute to the PSG’s cost recovery are sponsorship and advertisements. With the acquisition of Neymar, the French football club will receive lots of money through club sponsorship. Since Neymar is widely known and has a huge following on Instagram, his arrival will definitely lend to the club’s brand and will lure many companies to provide sponsorship. The second factor that is likely to contribute to PSG’s cost recovery is advertisements. Since Neymar is popular and has huge Instagram followers, many companies will prefer to use Neymar to advertise their brands thereby paying PSG lots in revenue collection.
Question Two
With three weeks of the transfer “window” left, teams in Europe’s “big five” leagues—the top divisions in England, Spain, Germany, Italy, and France—have paid €3.2bn, just short of the record of the €3.4bn set last year. How much percent is the €3.2bn short of the €3.4bn set last year?
Last year’s amount = €3.4bn
This year’s amount = €3.2bn
The percentage change is given by the formula below
Question Three
In three years, how much can the payment from Instagram pay for Neymar?
Instagram pays for Neymar €24m a year
After three years, the payment will be €24m X 3 = €72m
Question Four
If the €500m cost to PSG owners bears a total interest rate of £7% and if they pay an equal amount every year, how much will the owners have to pay each year during the five year period to pay off this debt in full?
Given that;
Initial cost = €500m
Total interest rate = £7%
British Pound to Euro exchange rate 1.14
Therefore;
Interest rate in sterling pounds = 1.14 X 7% = €7.98%
Total ineterst charges = 7.98% X €500m = €39.9m
Total amount = initial cost + total interest
= €500m + €39.9m = €539.9m
Equal payment over 5 years = €539.9m / 5 = €107.98m
So, the PSG owners will pay €107.98m every year for 5 years.
Task 2: In Class Activity (LO 1, 2 "3)
Question One
Let
Most expensive item by Y
Least expensive item be X
For the given information;
Y = £24 + X . . . . . . . (1)
X + Y = £27.7 . . . . . . (2)
Substituting equation 1 into 2 and solving yields;
X + Y = £27.7
X + (£24 + X ) = £27.7
X + X + £24 = £27.7
2X + £24 = £27.7
2X = £3.7
X = £3.7 / 2
X = £1.85
Therefore, the least expensive item costs £1.85, and
The most expensive item costs £1.85 + £24 = £25.85
Question Two
Suppose;
Price of large pizza = p,
Quantity supplied = q, and
The supply function is given by the equation below;
P = (q/50)
Writing the above equation gives the expression for quantity supplied as follows;
(q/50) = p; multiplying by 50
q = 50 p
Suppose the price, p = £18.75, the quantity supplied will be;
q = 50 p
q = 50 x £18.75
q = 937.5
But since quantity cannot be in a fraction, we round off to 938 large pizzas supplied.
Question Three
Suppose x is the number of credit hours and C is the cost of tuition at a community college, where the cost is given by the function;
C(x) = 490 + 54x
In the above function, the slope is 54. It represents the rate of change in the cost of tuition per credit hour. That is the tuition cost changes by £54 after every one credit hour. Since the rate of change is positive, the tuition cost increases by £54 after every one credit hour.
Question Four
Given the following;
List price = £250
Trade discount series = 12 % / 6 % / 3 %
Therefore, actual price per each discount
100 % - 12 % = 88 % = 0.88
100 % - 6 % = 94 % = 0.96
100 % - 3 % = 97 % = 0.97
Multiplying the trade discounts gives the net discount as follows
Net discount = 0.88 X 0.96 X 0.97 = 0.819
Therefore;
Net price = net discount X list price
= 0.819 X £250
= £204.8
Question Five
Let y be the number of pound sterling charged, and
x be the number of minutes the repair person is on the job
The cost of given by the model equation below;
y = 47.38 + 0.617x
Suppose y = £120,
Substituting for the value of y in the equation above and solving gives;
y = 47.38 + 0.617x
120 = 47.38 + 0.617x
72.62 = 0.617x
0.617x = 72.62
x = 72.62 / 0.617
x = 117.7 minutes
Approximately, it would take 118 minutes
Task 3: (LO 1, 2, " 3)
Question One
The relationship between the number of units sold by a company and the profit is linear. If 5 units sold results in £110 profit and 37 units sold results in £814 profit, find the marginal profit.
Let P represent profit and S represent sales
Given that P1 = £110, S1 = 5, P2 = 37, S2 = £814
Marginal profit is the rate of change in profit per rate of change in sales.
So, the marginal profit is 22.
Question Two
Given that;
S(x) = 80x + 3600 . . . . . . . (1)
Suppose S(x) = 4320, substituting back in equation 1 gives;
S(x) = 80x + 3600
4320 = 80x + 3600
80x = 720
x = 720 / 80
x = 9 years
Since x = 0 corresponds to 2010, we add the 9 years to 2010 which gives the year 2019. So, the sales will be 4320 in 2019.
Question Three
Given the cost equation below;
c(x) = 4 - 288x + 50 . . . . . . . . . . . . . (1)
where x is the number of watches repaired.
To find the minimum cost, we determine the first derivative of equation 1 above and then equate to zero.
c(x) = 4 - 288x + 50 .
dc/dx = 8x - 288
But at minimum cost, dc/dx = 0, therefore,
8x - 288 = 0
8x = 288
x = 288 / 8
x = 36
So, David must repair at least 36 watches in order to have the minimum cost.
Question Four
The manager of big box store has found that if the price of a pillow is p(x) = 95 - (x/8), then x pillows will be sold. The expression for the total revenue from the sale of x pillows is R(x) = 95x - (x to the power of ((2))/8). Find the number of pillows that will produce maximum revenue.
Let p be the price of the pillow
R be revenue
P be the price of a pillow
x is the quantity of pillows sold
Given that;
To proceed, we first calculate the marginal revenue, which is given by the first derivative of equation 2 above.
MR = dR / dx
= d/dx ()
=
However, at maximum revenue, the marginal revenue equals to zero. Therefore,
MR = 0
= 0
Solving the equation gives;
95 – 0.25 x = 0
0.25 x = 95
x = 95 / 0.25
x = 380
So, the company must produce 380 pillows in order to receive maximum profits.
Question Five
Let R be revenue
C be cost
X be the output level
Given that R(x) = 80x - 2x^2; C(x) = 24x + 100
Profit (π) is given by revenues less total costs, i.e.
Π = R – C
= (80x - 2x2) – (24x + 100)
= - 2x2 + 80x – 24x - 100
= - 2x2 + 56x – 100 . . . . . . . (1)
To find the profit maximization output, we get the first derivative of equation 1 above and equate to zero.
Π = - 2x2 + 56x – 100
d Π / dx = -4x + 56
But at maximum profits,
d Π / dx = 0, thus,
-4x + 56 = 0
4x = 56
x = 14
The profit maximizing output is 14. So, maximum profit is given by;
Π = - 2x2 + 56x – 100
= - 2 (14 x 14) + 56x 14 – 100
= -392 + 784 – 100
= 292
So, the maximum profit is 292.
Task 2: In class Activity (LO 2 "3)
Question One
Suppose t is the time in months
B is number of acres in a landfill
Given that t = 9 and that B is given by the equation below, then;
Substituting for the value of t we get
So, the landfill will have approximately 1849 acres of land in 9 months.
Question Two
The initial value of the dining set is $3900
Its value is given by the exponential equation below
At time t = 5 years, the value will be
So, the value of the investment after five would be $3,900 - $ 972.95 = $2927.05
Question Three
Assigning values for b, M, and N show that the following holds true.
= + . . . . . . . (1)
Let b = 10, M = 4, and N = 5
The left hand side gives;
Right hand side gives;
Since equations 2 and 3 have the same value, we conclude that equation 1 holds.
Question Four
Assigning values for b, M, and N, show that the following holds true.
= - . . . . . . . (1)
Let b = 10, M = 6, and N = 2
The left hand side of equation 1 gives;
The right hand side of equation 1 gives;
Since the value of equation 2 and 3 are the same, we concluded that equation 1 holds true.
Question Five
The number of visitors to a tourist attraction (for the first few years after its opening) can be approximated by V(x) = 40 + 100, where x represents the number of months after the opening of the attraction. Find the number of visitors 32 months after the opening of the attraction
Let x be the number of months
Let v be the number of visitors to the tourist attraction
Suppose v is given by the equation below
After 32 months, the number of visitors would be;
So, the number of visitors after 32 months would be 45.
Question Six
Given the following information;
The machine cost is £3700
The salvage value is £200
The estimated lifespan is 5 years
Total depreciable cost = machine cost – salvage value = £3700 - £200 = £3500
Annual depreciation amount = Total depreciable cost / Estimated lifespan = £3500 / 5 = £700
Depreciation schedule
Year
Book value at the start of the year
Depreciation expense
Accumulated depreciation
Book value at end of year
1
£3,700
£700
£700
£3,000
2
£3,000
£700
£1,400
£2,300
3
£2,300
£700
£2,100
£1,600
4
£1,600
£700
£2,800
£900
5
£900
£700
£3,500
£200
Question Seven
Find the cost of a jacket that has been marked up £30 and has a markup rate of 40%.
The markup price is £30
The markup rate is 40%
Markup = 40% of selling price = 0.4 X 30 = 12
Cost + Markup = Selling Price
Cost + 12 = 30
Cost = 30 – 12 = £18.
Therefore, the cost of the jacket is £18.
Question Eight
Find the excise tax on a £65 purchase of soft drinks, where the excise tax rate is 14.6%.
The exercise tax rate is 14.6%
Amount of soft drinks is £65
The exercise tax amount = 14.6% of £65
= 0.146 X £65 = £9.49
Question Nine
Find the sales tax for the mobile charger if the marked price is £9.50 and the total price is £12.45.
Given that;
The marked price is £9.50, and
The total price is £12.45, then
The sales tax = total price = marked price
= £12.45 - £9.50 = £2.95
So, the sales tax on the mobile charger is £2.95.
Question Ten
Find the property tax on a home with an assessed value of £280,000 if the property tax rate is 13.5% of the assessed value
Given that;
Home value is £280,000
The property tax rate is 13.5%, then
The property tax = 13.5% of the £280,000
= 0.135 X £280,000 = £37,800
So, the property tax is £37,800 for the home.
Task 3: (LO 1 " 2)
In the following, no working is needed. Just choose the one alternative that best completes the statement or answers the question. Highlight and make bold the letter and text of the correct answer. For instance, 1+2 = ? a) four b) three c) five d) six. If you agree the answer is three, highlight as shown.
1) The five office workers at Northern gas and electricity earned salaries last year of £14,000, £34,000, £38,000, £20,000, and £27,000. Find the mean salary.
A) £25,270 B) £27,930 C) £29,260 D) £26,600
2) The monthly net gains sales for a new electrical devices store were: £8561, £2811, £3199, £7100, £7593, £3322, £2332, £7405, £4979, £4327. Find the median.
A) £4653.00 B) £5736.56 C) £4979.00 D) £5162.90
3) If you were considering purchasing a low-priced home in London with home values ranging from £150,000 - £200,000 which of the following would give the most realistic picture of how much that home is likely to cost?
A) Mean B) median and mode C) grouped data D) class interval
Solve the problem.
4) The owner of a bakery employs six people. As part of their personnel file, he asked each one to record to the nearest km the round-trip distance they travel to and from work each day. The six distances are listed below. Find the variance rounded to the nearest tenth.
29 28 16 49 67 29
A) 28.9 B) 9374.4 C) 24.2 D) 338.3
5) Jane is currently taking college arts. The lecturer often gives the weekly test. On the past seven weekly tests, Jane got the following scores. Find the standard deviation.
50 20 42 29 19 48 71
The standard deviation is 18.6675
(10 marks)
SECTION 2 – Case Study
Question One
The following table shows the average number of grams of fat in various entrees served at a restaurant in Greenford area. Using Excel, construct a bar showing the number of grams of fat by entree.
Entree
No. of grams of fat
Mash Hash
20.1
Barnyard Plate
19.2
Peacs " Q’s
15.3
Bean O’Rama
9.6
Swiss Misty
17.7
Top Roundup
14.1
Wellness Platter
3.6
Good Karma
8.7
Bar graph
Question Two
The line graph below shows Tim's salary history during his first seven years at his current job.
What is the percent of the increase in Brett's salary between his sixth and seventh year at the job? You need to show the working.
Brett's salary in the sixth year =60,000 dollars
Brett's salary in the seventh year = 64,000 dollars
Question Three
Use the circle graph to solve the problem. The circle graph below gives the inventory of the women's department of a store.
In which item of apparel does the store have the smallest investment and the highest investment? Work out each as a percentage of the total.
§ The store has the smallest investment in the socks category, representing only $2,676.
§ The store has the highest investment in coats category, representing $38,133.
Question Four
The following table gives the weekly incomes of 15 workers in a company.
Workers
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
wages
205
202
215
206
209
210
212
220
240
211
216
218
214
210
204
Using Excel,
4.1. Calculate mean, median and mode
The mean, median and mode as calculated using MS Excel formulas are 212.8, 211, and 210 respectively. The excel file is attached.
4.2. Draw a histogram
4.3. Workout summary statistics and give an example of interpretation
Summary statistics
wages
Mean
212.8
Standard Error
2.360791
Median
211
Mode
210
Standard Deviation
9.143304
Sample Variance
83.6
Kurtosis
5.298382
Skewness
1.924352
Range
38
Minimum
202
Maximum
240
Sum
3192
Count
15
The summary statistics as calculated using MS Excel is presented in the table above. There is no significant between the mean, median and model meaning that the data lack significant divergence. The range and standard deviation are also small which justify the same. The skewness is substantial since it is greater than 1.0. the value 1.9 shows that the data is skewed to the left.
SECTION 3 – Reflection
Describe three skills you have developed on this module and comment on how you can use them to develop your career. Make a reference to the three skills audits you completed above (200-250 words).
Skills Developed
The first important skill I have developed in this module is how to summarize present data. I am able to summarize, group, and visualize large data for ease of presentation and basic statistical analysis. The skill is essential for my career development. For instance, the first thing I will do once a receive the data is to summarize, group, and visualize it. The skill will help me make good and impressive presentations and further enhance my statistical analysis in my career development. I will use the skill to present data in a way that it best tells a story.
The second important skill I have developed in this model is how to conduct the descriptive analysis. I have learned how to calculate and use descriptive statistics, in reality, using a various range of datasets. I have learned how to interpret and apply various descriptive statistics such as mean, mode, median, variance, and range among others. Descriptive analysis is essential for my career development because it will help me describe reality in the best way possible. In essence, in my career, I will be using descriptive statistics to describe the situation it is presented through data.
The third skill I have developed on this model is how to use MS Excel to perform mathematical and statistical calculations. The skill is essential because Excel eases mathematical calculations and statistical analysis. Instead of a calculator, I will be using MS Excel throughout my career to perform such statistical calculations.
