Numeracy 2 Portfolio: Financial Mathematics and Data Interpretation

This Numeracy 2 portfolio assignment assesses understanding of financial mathematics and data analysis. Section 1, worth 75% of the final mark, contains eight questions covering powers, roots, simple and compound interest, linear relationships, the future value of money, net present value, presentation of data, and probability. Students are required to show their workings and explain their results. Section 2, worth 25%, includes two real-life examples, an online activity, and a reflective log. The assignment covers topics such as simplifying powers and roots, calculating interest (simple, compound, semi-annually, and quarterly), solving equations, creating and interpreting linear graphs, calculating net present value, producing and interpreting histograms, and calculating probabilities. The solutions demonstrate the application of these concepts to real-world financial scenarios, like investments and the valuation of business projects. The assignment emphasizes the importance of showing all working and provides detailed explanations, including references to relevant sources.

Numeracy 2
·

Academic Misconduct
You are responsible for ensuring you understand the policy and regulations about academic
misconduct. You must:
壱Complete this work alone except where required or allowed by this assignment briefing paper
and ensure it has not been written or composed by or with the assistance of any other person.
弐Make sure all sentences or passages quoted from other people’s work in this assignment (with
or without trivial changes) are in quotation marks, and are specifically acknowledged by
reference to the author, work and page.
This portfolio consists of two sections:
Section 1 is worth 75% of the final mark and consists of 8 questions (70%) and periodic Skills
Audit (carrying 5%).
Section 2 consists of 3 tasks. Combined they are worth 25% of the final mark.
Task 1 – Two Real life examples (8%)
Task 2 – Online Activity (10%)
Task 3 – Reflective log (7%)
Portfolio Contents
1Week / ContentSection 1 QuestionLearning
OutcomePageSection 1Recap numeracy 1. Introduction.
Powers. Use of calculator1 *1,2Powers, root, logarithms.
Use of calculator2 *1,2Simple & compound interest 13,4
*1,2Linear relationships. Scatter plots.5 *1,2,3Further
linear relationships5 *1,2,3The future value of money.
Net present value.6 *1,2Presentation of data.
2

Histograms.7
*1,2,3Probability.8*1,2RevisionNone1,2,3Section 2Real-
Life ExamplesN/A1,3Online ActivityN/A1,2,3Reflective
LogN/A1,2,3
* Also assessed in the online quiz, Section 2, Task 3
Section 1
This section should be filled in as you acquire the skills required for each question.
Answer all questions. Please show your workings and/or explain your results as required.
Marks will be awarded for good presentation. Please evaluate your progress using the skills
audits provided.
You may use your calculator as required.
You must show your working.
QUESTION 1 [6 marks]
Powers and Roots:
a) Simplify (2 marks)
b) Simplify (2 marks)
c) Evaluate (2 marks)
Q1:
In numerical terms power of a number shows vital information about total time which is
being use that particular number is multiplied. This is represented by using small digits to right
and above base value. Other digit of power is said to be index or exponent. It is said to be that
specific value than 0 which is taken as zero(0) power and define as 1 (Venkat and Naidoo,
2012). For the purpose of simply power of a number, exponent has to be multiplied through
keeping similar base. Such as:
Simplify (6.0*105) / (25*10-4)
=(60*104) / (25*10-4)
Negation of 60= 15*4 and applying the formula of am/an=a m-n
= 4*104-(-4)

= 4*108
Root: It is known as effective root of a digit X to another number that is being multiplied
as itself in various manner. A more effective word to which affixes are taken into account as root
of that number. Such a example, second root of 3 is thrice, because 3*3=9. This has been seen as
clear that other root are always determine as square root of that particular digit.
Evaluating square roots: This will be simply as perfect means that is use to analyse total
value of mentioned data. Such as:
=?3+1= 2.73
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QUESTION 2 [8 marks]
a) Express the power 100
1/2
using the root notation and evaluate. (2 marks)
b) Evaluate (2 marks)
c) Simplify 7 (2 marks)
d) Scientific notation allows one to express large or small numbers in a simpler form.
Express the UK population of 65,648,000 in a scientific notation (2 marks)
[Q2:
(a): It has been observed that every non-negative real number has specific set of square root that
has been determine as perfect square of a number. It has been represented as
=1001/2
= 10.
(b): A square root is said to be effective number which is used to multiply with itself to make
proper values. It is more easy to identify as written symbol which has been useful to examine
amount and other specific value.
(c): In order to evaluate 7 there are different ways through which it can be represented. It has
been shown underneath:
Round it off:
Create zeros: In this case, 7 becomes 10.
[d]: Calculation of scientific notation
=6.5648×107
=6.5648e7
=65.648×106
=65648000
(real number)]
QUESTION 3 [10 marks]

Ann Miller invests £150,000 at an interest rate of 6% p.a.
Calculate the final balance after 5 years.
a) Using simple interest? (1 mark)
b) Using interest compounded annually? (3 marks)
c) Using interest compounded semi-annually? (3 marks)
d) Using interest compounded quarterly? (3 marks)
[Q3:
(a): Simple interest: It is said to be interest amount calculated only on principles not at principle
plus earned incomes in the previous time (Skwarchuk, Sowinski and LeFevre, 2014). It is
basically, helpful in variable rate as consumer lending and mortgage loans are borrowed through
paying interest amount only on capital used.
Formula: SI: P*R*T/ 100
=SI: 150000*0.06*5
: $45000
Normally, the interest is enclosed onto the first amount of digits which is measured with
6% rate. The new sum in 5 year they will get is:
=150000+45000= 195000.
(b): Interest compounded annually: It is said to sum of interest which is included into the
principles amount of total investment. This seems to be valuable results of re-investing interest,
instead of profit it is calculated underneath:
Formula: A= P(1+r/n)nt
YearYear InterestTotal DepositsTotal
InterestBalance1$9,000.00$150,000.00$9,000.00$159,000.002$9,540.00$150,000.00$18,540.0
0$168,540.003$10,112.40$150,000.00$28,652.40$178,652.404$10,719.14$150,000.00$39,371.
54$189,371.545$11,362.29$150,000.00$50,733.84$200,733.84(c): Interest compounded in
semi-annually rate:
This can be evaluated with effective rate of interest which is said to be 6.09%
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YearYear InterestTotal
InterestBalance1$9,135.00$9,135.00$159,135.002$9,691.32$18,826.32$168,826.323$10,281.5
2$29,107.84$179,107.844$10,907.67$40,015.51$190,015.515$11,571.94$51,587.46$201,587.4
6(d): Interest compounded quarterly:
This can be evaluated with effective rate of 6.14%.
1.1YearYear InterestTotal
InterestBalance1$9,204.53$9,204.53$159,204.532$9,769.36$18,973.89$168,973.893$10,368.8
4$29,342.73$179,342.734$11,005.11$40,347.83$190,347.835$11,680.42$52,028.25$202,028.25

QUESTION 4 [10 marks]
a) Eliza invests £22,000 at a 2% interest rate annually.
Compounding the interest annually, how long will it take her
to receive the balance of £33,000?
(4 marks)
b) Using Rule 72, calculate how long will it take Eliza to double her investments?
(2 marks)
c) Mr Ramsbottom invests £32,000 in a bank savings account and after 10 years his
balance is £45,200.20.
Calculate the compound interest rate he received and round your answer to the
second decimal place.
(4 marks)
(a): FV= PV(1+r)n
33000=22000(1+0.02)n
= 20.5
This would be approximately 20 years 5 month and 22 days for the account to reach from
22000 to 33000.
(b): According to the rule of 72, this will provide concept of simple regarding total amount
which is going to double investments.
Y = 72 / r
y= 72/2 =36
(c): In accordance with total saving account which would be invested in bank to get compounded
annually with total principle value of $32000 (Hess, Visschers and Siegrist, 2011). There will be
increment of $45200.2 after 10 years with total interest rate of 3.5% per annum.
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QUESTION 5 [8 marks]
a) Find the value of x if (1 mark)
b) Solve the equation X + 20 = 70 (1 mark)
c) Solve the equation = 10 (1 marks)
d) To plot the linear graph of y = 3x + 10 complete the following table:
x- 8-5071224y
(NO graph required)
(5
marks)
(a):
Value of X, if X= (2*3)+11
X= 6+11
X=17
Sp the value of X is said to be 17.
(b): Equation
X+20=70
X=70-20
x=50
[c]: Solve equation which is equal to 10
10-2=m/4+2-2 subtract 2 from both side
8=m/4
m=32
Check,
10=m/4+2
10=32/4+2 Substitute 32 for
10=8+2
10=10
[d]:
X-8-5071224Y-14-510314682

Question 6 [10 marks]
Sarah Hair Saloon is considering an investment project to purchase and run a Hair Saloon
business. The initial cost is £55,000. The annual cash inflows (income) are projected to be as
follows:
Year 1Year 2Year 3Year 4£15,000£25,000£45,000£15,000
The discount rate for this investment is 8% p.a., compounded annually.
a) Work out the Net Present Value (NPV) of this investment. (8 marks)
b) Should Sarah proceed with this project?
Explain your reasoning. (2 marks)
[Q6.
(a): Computation of NPV
YearCash flows PV factor @ 8% Present value 0-550001-
550001150000.925925925913888.88888888892250000.857338820321433.47050754463450000
.79383224135722.45084590764150000.735029852811025.4477919468100000Total present
value82070.2580342879NPV27070.2580342879(b): Recommendation
From the above calculation, it has been observed that with the total initial investment of
55000 they are able to earn valuable amount of net present value of 27070. This means that they
are having sufficient amount of capital after 4 year with health rate of return. The idea of
opening Hair Saloon Business is more reliable and effective proposal for the company.
Question 7 [10 marks]
A set of test scores, marked out of 100, is as follows:
66937558685365929462637493929558946278966264876657
a) Produce a tally of this data set suitable for the production of a histogram (3 marks)
b) Draw a histogram of this data set (6 marks)
c) Comment on the distribution of these marks. (1 marks)
10

Q7
(a): Test score
SubjectsTotal MarksABCDEMath 1006693755868Science 1005365929462Social
science1006374939295English1005894627896Literature1006264876657Total
500302390409388378
(b): Formulation of Histograms
It is said to be one of the effective charts which is utilized for controlling different data,
where the bins will indicate different range of respective variables. The most reliable support of
this histograms is to make evaluation of charts for the purpose of determining overall
frequencies of scores those are present in regular data series.
(c): Interpretation
According to the above information collected from the histograms charts, it has been
seen that there is huge fluctuation in relationship of marks collected by the students. The
histograms provide sample value that are said to be effective clustered which is presented on the
left side of histograms. The distribution are done as normal basis. These are said to be
frequencies of scores occurred in a regular basis in a given data series.
Question 8 [8 marks]
Probability is a measure of the likelihood and can be stated as a ratio, percentage or generally as
a number between zero and one.

a) What is the probability when the likelihood is impossible? (1 mark)
b) What is the probability when the likelihood is certain? (1 mark)
c) Express the probability of 0.06 as a % (2 marks)
d) Josiah tossed a coin and thrown a die at the same time (simultaneously). Work out the
probability of getting a head on the coin and a 5 on the die.
(4 marks)
Q8:
(a): In case of given activities is likely to be happen the chances of getting positive results would
be increased. This is use to measure overall ratios in best and suitable manner. Thus, the total
number of elements is provided as set of favourable condition which is <=1.
(b): This has been observed that likelihood will operate more often and common likelihood that
is based on set parameters under a statistical model in a given data series. The likelihood is
basically, a ratios of probably that has test results which is right to best probability that are come
out as incorrect (Woodford, 2011).
(c):
The probability of 0.06 which represented as 0.94%.
(d):
In case of coins, it has been seen that only 2 best possible results can be possible. [Head, Tail]
whereas in case of dies having 6side has maximum of total 6 outcomes. Such as, [1,2,3,4,5,6]
= 2*6=12, The possible results are:(Head, 1), (H, 2), (H, 3), (H,4), (H,5), (H, 6), (T,1), (T, 2), (T,
3), (T, 4), (T,5), (T,6)
Probability: 2/12= 1/6.
l弐Audit is covered in Appendix
Section 2
Task 1 - Two Real life examples (100 words each) [8 marks]
Give two real-life situations or problems in businesses that involve the topics studied in this
module (e.g. powers and roots, simple and compound interests, linear relationships, graphs,
probabilities and Net Present values (NPV)).
12

Two real life examples
On an assumption, XYZ company wants to make investment in their other projects. For
this purpose, they have invested certain amount as initial investments for 5 years (Fu and et. al.,
2013). The wants to known net present value of their investments.
YearCash outflowsCash inflowsPresent value0-1000001-
100000120003000028000250003000025000350003000025000450003000025000520003000028
000-81000150000131000NPV31000
In case of loan
It has been seen that, a car loan are said to be amortised on monthly terms that is based
on certain portion of loan that are going to pay as outstanding balance in every month.
I= P*R*T
= 20000*0.02*5
=2000
Total amount after completion of 5 years = 20000+2000
= 22000.
·Task 2 - Online Activities [10 marks]
This relates to the quiz. Please complete and pass all three relevant quiz/activity; screenshot and
save the result’s screen ready to be pasted on the portfolio.
Ensure the followings are visible before the screenshot:
·Your full names on the top right-hand corner of the screen
·Your test result is any score from 40% to 100%

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16

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·Task 3 - Reflective Log (150 words) [7 marks]
This reflective log should develop as the course proceeds, and may be the last part to be
completed. Reflect honestly on your experiences throughout the semester. Start your reflective
log from week one by completing the skills audits and by writing personal weekly notes after
each topic. Please ask for your Tutor’s support if needed.
You may wish to consider the following points when providing your reflective comments:
·Which topics do you feel most confident about? (e.g. powers and roots, interest rates, NPV
etc.)
·Are there areas for improvement (e.g. in probability, I need do practice more or research etc.)?
·How would you evaluate your participation on the module (e.g. contribution to classes,
independent study etc.)?
Reflective log

From the above project report I have analysed that, all those specific types of techniques
and approaches are being used are more effectively helpful in any given situations. The
outcomes are collected from one weak through analysing proper skill audits and formulating
continuous notes.
·Out of all topic that are provided above, I think the most interesting and useful topic is related
with NPV which I learned more effectively. I guess more easy to determine total return and
value of given portfolio investments.
·Yes, I think there are certain problems with analysis and understanding of probabilities which is
hard to determine the exact value of a given situations.
·The evaluation would be done by contributing data into classes. This will assists in better
understanding of necessary outcomes in more easy manner.
·CONCLUSION
From the above project report, it has been concluded that various numerical aspects
related in Numeracy 2. It will be analyse through using various financial information that are
helpful in taking more reliable outcomes during the time.
·
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·REFERENCES
Books and Journals:
Venkat, H. and Naidoo, D., 2012. Analyzing coherence for conceptual learning in a Grade 2
numeracy lesson. Education as Change. 16(1). pp.21-33.
Skwarchuk, S. L., Sowinski, C. and LeFevre, J. A., 2014. Formal and informal home learning
activities in relation to children’s early numeracy and literacy skills: The development
of a home numeracy model. Journal of experimental child psychology. 121. pp.63-84.
Hess, R., Visschers, V. H. and Siegrist, M., 2011. Risk communication with pictographs: The
role of numeracy and graph processing. Judgment and Decision Making. 6(3). p.263.
Woodford, M., 2011. Interest and prices: Foundations of a theory of monetary policy. princeton
university press.
Fu, J. and et. al., 2013. NPV-LDE-225 (Erismodegib) inhibits epithelial mesenchymal transition
and self-renewal of glioblastoma initiating cells by regulating miR-21, miR-128, and
miR-200. Neuro-oncology. 15(6). pp.691-706.

SKILLS AUDIT: WEEKS 1 – 2I know how to….I can do wellI need practiceI’m not sureI
can’t doI understand what a power isYES???I can perform calculations and simplifications
using powerYES???I understand what a root is?YES??I can perform calculations and
simplifications using roots, using a scientific or financial calculator if required??YES?WEEKS
3 – 4I know how to….I can do wellI need practiceI’m not sureI can’t doI understand the idea
of simple interestYES???I can perform simple interest calculationsYES???I understand the idea
of compound interestYES???I can perform compound interest calculations using a calculator if
required?YES??I understand the Rule of 72 (or 69 or 70) and can apply it.YES???WEEK 5I
know how to….I can do wellI need practiceI’m not sureI can’t doI understand the idea of a
linear relationship between two variablesYES???I can manipulate a linear equation to solve for a
variable?YES??I can construct a scatter plot from a set of data (a linear relationship applies) and
apply a line of best fit.?YES??I understand the y-intercept and slope (gradient) of a graph and
their meaning to real situations ().??YES?I can use the scatter plot produced in part (12) to
derive a linear relationship between two variables ().?YES??I can use the relationship from part
(14) to extrapolate and interpolate??YES?WEEK 6I know how to….I can do wellI need
practiceI’m not sureI can’t doI understand the idea of the future value of moneyYES???I
understand the idea the net present value (NPV) of a projectYES???I can complete a net present
value calculation, using a calculator if requiredYES???WEEK 7I know how to….I can do
wellI need practiceI’m not sureI can’t doI understand the idea of frequency
distributionYES???I can read and interpret a histogram?YES??I can construct a histogram from
a set of dataYES???WEEK 8I know how to….I can do wellI need practiceI’m not sureI
can’t doI understand simple probabilitiesYES???I can perform probability calculations, using a
calculator if required?YES??I understand and can perform exchange rate calculations??YES?
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