Financial Mathematics Assessment

This assignment evaluates knowledge in various financial mathematics concepts. Students demonstrate understanding of simple and compound interest calculations, the Rule of 72, linear relationships, present value, and basic probability. Tasks involve performing calculations, constructing graphs, and interpreting data. Proficiency with calculators is expected for certain problems.

Numeracy 2 E-Portfolio
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Please read this carefully
This is your Numeracy 2 e-portfolio for the semester commencing February 2018 (Spring 2018). Please
save a copy on your computer and back it up regularly (e.g. by saving it on your computer / in the cloud
(e.g. Google Drive) / emailing it to yourself. You should print a working copy and bring it to all lectures
and tutorials. However, at the end of the course, you will need to submit a completed electronic copy.
Please read carefully the module handbook, the marking criteria and the grade descriptors.
Academic Misconduct
You are responsible for ensuring you understand the policy and regulations about academic
misconduct. You must:
l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.
l壱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%)
2

Portfolio Contents
Table of Contents
INTRODUCTION....................................................................................................................... 4
SECTION 1................................................................................................................................. 4
QUESTION 1 .......................................................................................................... 4
QUESTION 2 .................................................................................................................. 5
QUESTION 3 ................................................................................................................... 5
QUESTION 4 ............................................................................................................ 7
QUESTION 5 ................................................................................................ 8
Question 6 ............................................................................................................... 8
Question 7 ............................................................................................................... 9
Question 8 .............................................................................................................. 10
Auditing part is done in Appendix .................................................................................... 11
SECTION 2............................................................................................................................... 12
Task 1 - Two Real life examples ....................................................................................12
Task 2 - Online Activities ............................................................................................ 12
Task 3 - Reflective Log ............................................................................................. 13
CONCLUSION ......................................................................................................................... 14
REFERENCES.......................................................................................................................... 15
APPENDIX: 1........................................................................................................................... 16

l壱INTRODUCTION
Numeracy segment provide various understanding of technicals and analytical aspects
that will be helpful to determine various positive outcomes. The project report provide various
information about various financial techniques such as investment appraisal tools and other
crucial financial systems. This consists of two sections of their respective data evaluation.
l壱SECTION 1
l弐QUESTION 1
Powers and Roots:
a) Simplify (2 marks)
b) Simplify (2 marks)
c) Evaluate (2marks)
[a]Power: It is a number which indicate about total times which uses the number in a
multiplication. This is shown as a small number to the right and above base number. The another
name of power is index or exponent. A number which is other than 0 is taken to the power 0
which is define to be 1. In order to simply power of a power , exponent has to be multiples by
keep the base same. Like for example: (xa)b= xa·b, in case of any positive number X and
integers a and b the above equation would be taken into account.
Problem 1:
Simplify (6.0*105) / (25*10-4)
=(60*104) / (25*10-4)
Cancellation of 60 with 4 times 15 and applying the formula of am/an=a m-n
= 4*104-(-4)
= 4*108
4

[b] Root: It is known as root of a number X is said to be another number which is being
multiplied by itself in so many time. A basic word to which affixes are taken into consideration
as root. Like for example, second root of 4 is 2, because 2*2=4. From this, it has been clear that
second roots are always count as square root.
[c] Evaluating square roots: It is simply means that to calculate value of the given problems.
Such as ?3+1
c) =1.73+1=2.73
l弐QUESTION 2
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)
[A]: It has been seen that every non-negative real number has unique square root which
determine as square root. It has bee denoted by ?a, where ? is said to be radical sign.
=1001/2
=?100
= 10.
[b]: A square root is known as effective number which is a number that can multiply by itself to
a proper value. It is simply determine as written symbols which is used to indicate amounts and
any other value.
[c] In order to simplify 7 there are various ways which is being present 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)
l弐QUESTION 3
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)
[a]: Simple interest: It is known as one of the simple and quick method to computer the interest
charges on the principles amount. It is determine by multiplying the everyday interest rate
through the principles with total number of days available among payments.
Formula: SI: P*R*T/ 100
SI: 150000*0.06*5
: $45000
Usually, the interest is included onto the initial amount of figures which is calculated
with 6% rate. The new amount of 5 year they will get is:
=150000+45000= 195000.
[b]: Interest compound annually: It is know as total addition of interest which is added to the
principles total of investments. This happens to be outcome of reinvesting interest, rather than
gainful it out. 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 semi-annually:
Effective rate of interest charges with the rate of 6.09%
6

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
Effective annual rate of 6.14%
YearYear 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$202,028.2
5
l弐QUESTION 4
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
It will be take approximately 20 years 5 month and 22 days for the account to go from
22000 to 33000.
[b]: Rule 72 provide simple concept about total amount which is going to double investments.
Y = 72 / r
y= 72/2 =36
[c]:
In case total savings account which is being invested in the bank compounded yearly
with principles amount of $32000. After 10 years, the total amount increase to $45200.2. they
would get 3.5% of interest per annum.
l弐QUESTION 5
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-14-510314682
(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
l弐Question 6
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)
8

[a]: Calculation 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
On the basis of above calculation, it has been found that from the total initial investments
of 55000 with different cash flows in each year. They are getting a positive net present value of
27070. This means that they are sufficient enough of return after four year so they this proposal
is more reliable and effective for their Hair Saloon businesses.
l弐Question 7
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)
[a]: Tally of data
SubjectsTotal MarksABCDEMath 1006693755868Science 1005365929462Social
science1006374939295English1005894627896Literature1006264876657Total
500302390409388378
B): Preparation of Histograms
It is known as effective charts which is used for regulating various data, where the bins
indicate various range information. The major difference of using histograms is only to make use
for the purpose of plotting overall frequency of score those are available in regular data series.

c): Interpretation:
From the above information collected from the data provide vital outcomes after preparing
histograms charts. The results are more clear that there is huge fluctuation in the total marks
collected by various student from that particular test. The histograms graphs provide vital
outcomes that maths, science and social science is provide more effective percentage in total
100.
1
l弐Question 8
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)
[a]: Probabilities by their own explanation is level to which an activities is likely to be happen. It
use to measure overall ratio of favourable cases to the entire number of cases in best possible
manner. Henceforth, number of components is the overall set of favourable situations which is
10

less than or equal to the number of elements in a given data series. The ratios would in that
condition ends with 1 and less than 1.
The major point is that, probabilities equals only when favourable number in a given case
are similar as that of the whole number of situations. Definitely, it is not possible that it become
zero. It is defined as likelihood or any modification of arises in an given activities. Few events
are unlikely to be arises through not impossible during other conditions which is more likely to
be occurs.
B]:
It has been seen that a likelihood operate often simply the likelihood which is based on
the parameters of a statistical model in a particular data. The scale values in a specific data
range such as the actual probabilities of a data would provide parameters value. The LR are used
to assess various crucial things such as potential utility of a specific diagnostic test. Likelihood is
generally, a ratio of probably that test outcomes is correct to the best probability that test results
is incorrect.
c):
The probability of 0.06 is represent 0.94%
d]: Probabilities:
For a coin, there are 2 possible outcomes is possible such as= [Head, Tail]
In case of die which is having ( 6 sided) so a maximum of 6 possible results =[1,2,3,4,5,6]
Now, when coin is tossed and die is rolled at the same time, 2*6=12 possible outcomes can be
attain. Such as,
(Head, 1), (H, 2), (H, 3), (H,4), (H,5), (H, 6), (T,1), (T, 2), (T, 3), (T, 4), (T,5), (T,6)
So after analysing, all these results it has been seen that the chances of getting head is 2.
Probabilities= 2/12=1/6.
l壱Auditing part is done in Appendix
l壱SECTION 2
l弐Task 1 - Two Real life examples

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)).
(1) Let's assume Company XYZ wants to acquire another company ABC. For this purpose they
have taken estimation of their last 10 year performance. As NPV is said to be an effective
investment appraisal techniques which can be helpful for the company's in order to make
analysis of their actual return they are getting in present time. The below mentioned is the case
situation which would provide well effective information about their financial position by seeing
those XYZ company will decide whether to make accept this proposal.
YEAR Cash inflows Initial investment
10000001200000215000031000004750005650006500007450008300009250001015000Total
755000NPV245000
In case of car loan:
It has been seen that car loan are amortised on monthly basis, which means that a certain
portion of the loan will go on to pay outstanding loan balance every month. Like for example: It
assume that a car loan of $ 20000 on which a simple interest is going to be payable at 2 %. The
loan would repaid after 5years in equal instalments.
I= P*R*T
= 20000*0.02*5
=2000
Total amount after completion of 5 years = 20000+2000
= 22000.
This much amount they are going to be gain over there total principles amount of 20000.
Usually in recent time, the interest is included onto the amount to determine exact figure after 5
years.
l弐Task 2 - Online Activities
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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l弐Task 3 - Reflective Log
From the above project report analysis, it has been found that there are various types of
techniques and method which are helpful in determining the overall results for the given
situation. The results are taken from week one by evaluating skill audits and preparing weekly
notes.
From WEEK 1-2: The maximum results are indicating overall learning experience that I
collect from the mentioned scenario. As better understanding of power and roots to resolve
various questions would provide effective solution in quick time. The overall outcomes are
providing best and reliable knowledge that I have utilised in solving those questions.
In WEEK 3-4: In next week, the analysis goes directly on evaluating simple and
compound interest formula. This will assists in determine and increase ability to examine exact
amount and interest of my principles values. Learning of both interest topic can lead to develop
my inner skills and ability.
WEEK 5: The 5th week target is to learn various types of linear relationship those are
exist in two variables. I have found easy ways to calculated various equation but in some
situation it is difficult to deal with. The charts of the mentioned data is hard to design.
WEEK 6: Under this, time period use of investment appraisal techniques in order to
make evaluation about overall return which is being collected out of my overall investments. I
have not any issue regarding computing NPV of the given data.
WEEK 7-8: This is the only time, I have faced major issues about tally of data. It will
leads to many problems in preparing histograms charts. This has seen so much impacts because
of unequal distribution of data in frequency table. In the last week, I have studied about various

mathematical question regarding probabilities ratios and their likelihood. There is huge
difference in their learning experience.
The overall knowledge, I have gained from this project will provide me perfect
experience about various aspects that results in solving various issues.
l壱CONCLUSION
From the above project report, it has been concluded that Numeracy2 information. This
would guide managers to evaluate various financial aspects those are helpful for better decision-
making. This report consists of crucial information regarding financial tools and techniques
which will assists in attaining future growth and sustainability for the company.
l弐
14

l弐REFERENCES
Books and Journals:
Shomos, A., 2010. Links between literacy and numeracy skills and labour market outcomes.
Sirota, M. and Juanchich, M., 2011. Role of numeracy and cognitive reflection in Bayesian
reasoning with natural frequencies. Studia Psychologica, 53(2), p.151.
Daraganova, G., Edwards, B. and Sipthorp, M., 2013. Using National Assessment Program
Literacy and Numeracy (NAPLAN) Data in the Longitudinal Study of Australian
Children (LSAC). Department of Families, Housing, Community Services and
Indigenous Affairs.
Black, S. and Yasukawa, K., 2011. Working Together: Integrated language, literacy and
numeracy support in vocational education and training. Centre for Research in Learning
and Change, Faculty of Arts and Social Science, University of Technology Sydney.
Nickisch, K. and Bode-Greuel, K.M., 2013. NPV modelling for the selection of value-creating
biosimilar development candidates. Journal of Commercial Biotechnology. 19(1).
Kerzner, H. and Kerzner, H. R., 2017. Project management: a systems approach to planning,
scheduling, and controlling. John Wiley & Sons.

l弐APPENDIX: 1
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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