Numeracy Assignment: Financial Concepts and Data Interpretation

This numeracy assignment solution encompasses a range of financial and mathematical concepts. It begins with an exploration of the laws of indices, simplification of expressions, and evaluation of examples. The assignment then delves into root laws, including square, cube, and fourth roots, and provides a scientific notation example. Further, it covers simple and compound interest calculations, including annual, semi-annual, and quarterly compounding. The solution also addresses the time required for an investment to double, the calculation of compound interest rates, and the concept of Net Present Value (NPV). The assignment includes a tally of data, a histogram, and comments on marks distribution. The solution also addresses the application of these concepts in real-life scenarios, such as project feasibility and investment decisions.

NUMERACY 2

SECTION 1
QUESTION 1
A. Three laws of indices
In order to manipulate and exaggerating values which are involved under the indices,
there are rules and methods are used which identified as laws of indices. Basically, there are
three kinds of laws and rules included under the indices which are such as follows:
1. First law: In the first law of indices, value of power differs but base value remains constant.
Further, multiplication of same base amount or value is done at the first law of indices.
2. Second law: Under the second law, the value which are same taken into base and divided.
Further, power get change and differ of same base.
3. Third law: As per the third law, values of power like m and n are to be multiplied with the
yield or frame of new index like mn.
B. Simplification of the laws
1. First law:
6^5 * 6^4
= 6^5+4
= 6^9
2. Second law:
9^6 / 9^2
= 9^6-2
1

= 9^4
3. Third law:
(5^4)^3
= 5^4*3
= 5^12
C. Evaluation
1. First law: In this law of indices there are power values are added of the base value which are
same and then go for performing further solution. Whatever comes by adding power values of
same base, that will be used to calculate. In this case, base value is 6 and power of it will be such
as 9 (5+4).
2. Second law: When looking at the example of second law of indices then it can be found that
power are subtracted at the time of base values divides. Here also base value must remain same
of different power laws. Moreover, base is 9 on which power apply is like 4 (6-2).
3. Third law: In the case of third law of indices, power of base and whole bracket are multiplied
and then solution is applied. From the above example it can be seen that power of base and
bracket are like 4 and 3 respectively which are multiplied and then apply in base which is 12
(4*3).
QUESTION 2
A. Three examples of root laws
Root shows fractional values of indices and digits which are multiplication of the same
value. It includes generally three kinds of rules and laws which are listed below:
1. Square root: √16 = 4
2. Cube root: 3√8 = 2 (2*2*2)
3. Fourth root: 4√2401 = 7 (7*7*7*7)
2

B. Evaluation
1. Square root: Under this law of root, number which comes in terms of output is multiplication
with itself of the question value. Further, answer value under the square root is multiplied by
itself of the give digit.
2. Cube root: As per this respective law, number or digit is produced and outcome is cubed of
the given number. Further, it can be said that, cube root is the outcome derived after making
multiplication of the initial value up to the three times.
3. Fourth root: In the rule of fourth root, outcome is multiplication of 4 times itself where
before the root sign 4 value is stated. In the simple way, when particular value multiplied itself
up to the four times and outcome is considered as the fourth root under the law of roots.
C. Scientific notation of 6,80,000
When a particular or specific value needs to write down in small way then scientific
notation is used which is the mostly used by businesses. At the current study 6,80,000 digit is
given and in the scientific notation it writes in small ways which is given as below:
680000 = 6.8 * 10^5
Here 10^5 is derived from the digits which come after the first value.
Weeks 1-2
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
11 I understand what a power of a number is ☐ ☐ ☐ ☐11 I can perform calculations and
simplifications using indices
☐ ☐ ☐ ☐11 I understand what a root of a number is ☐ ☐ ☐ ☐11 I can perform calculations and
simplifications using roots, using a
scientific or financial calculator when
required
☐ ☐ ☐ ☐
3

QUESTION 3
A. Simple interest
Principle amount £50,000.00
Interest rate per annum 3.00%
Time 5 years
Simple interest P*R*T / 100
= 50000 * 8 * 5 / 100
= £20000
B. Annually compound interest
C = P [(1+r)n – 1]
= 50000 [(1+0.03)5 – 1]
= 50000 * 0.1592
= £7960
C. Semi-annually compound interest
C = P [(1+r/2) 2*n – 1]
= 50000 [(1+0.03 / 2) 2*5 – 1]
= 50000 * 0.1605
= £8025
D. Quarterly compound interest
C = P [(1+r/4) 4*n – 1]
= 50000 [(1+0.03 / 4) 4*5 – 1]
= 50000 * 0.1612
= £8060
4

QUESTION 4
A. Time taken to become investment amount double
Principle £80000
Interest rate 4.5% annually
Double amount £160000
Time C = P [(1+r)n]
160000 = 80000 (1+0.04.5)n
= 15.8 years
When looking at the law or rule of 72 to calculate number of years then time period
required to get double amount of initial investment will be 16 years which is as follows:
72 / 4.5 = 16 years
B. Calculation of compound interest rate
Principle £8000
Time 10 years
Balance £9751.96
Interest rate C = P [(1+r)n]
9751.96 = 8000 (1+r)10
= 2%
Weeks 3-4
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do11 I understand the idea of simple interest ☐ ☐ ☐ ☐
5

11 I can perform simple interest calculations ☐ ☐ ☐ ☐11 I understand the idea of compound
interest
☐ ☐ ☐ ☐11 I can perform compound interest
calculations using a calculator if required
☐ ☐ ☐ ☐11 I understand the Rule of 72 (or 69 or 70)
and can apply it in context.
☐ ☐ ☐ ☐
QUESTION 5
I have very basic and general idea about the linear equation and in order to understand
about the relationship of linear among two or more variables I require practice. Along with this,
it can be said through current self-assessment that, I cannot perform and make calculation of
those equations which are given in the current question. Along with this, there is lack of
availability of knowledge regarding to the scatter diagram and its interpretation. Therefore, the
questions of linear equation are not attempted.
Week 5
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
111 I understand linear relationship between
two variables
☐ ☐ ☐ ☐
111 I can work out linear equation problems
given in this session
☐ ☐ ☐ ☐
111 I can plot a scatter graph from a set of
data
☐ ☐ ☐ ☐
111 I understand the y-intercept and slope
(gradient) of a line graph and interpret
☐ ☐ ☐ ☐
6

their meaning in real situations ().
111 I can use scatter plot to derive a linear
relationship between two variables ().
☐ ☐ ☐ ☐
111 I am able to explain the use of scatter
graphs in business context
☐ ☐ ☐ ☐
QUESTION 6
A) Calculation of NPV of the investment project
Year
Annual cash inflows of
the project
Discounting rate
@ 8%
Present value of the
project
Initial investment £70000
1 14000 0.926 12963
2 15000 0.857 12860
3 25000 0.794 19846
4 20000 0.735 14701
Summation £60369
Less: initial cost
of project 70000
NPV -£9631
B) Advise to the ATOB Trading Limited
From the above calculation of deriving net present value of the project it can be analysed
that, value of NP is worth of -£9631 which is negative. Further, negative nature of value shows
that investment will reduce the amount which is invested at the initial. Hence, it can be advised
to the management of ATOB Trading Limited company that, it needs to ignore the project and
should not purchase the machine.
7

Week 6
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
111 I understand the concept of the future
value of money
☐ ☐ ☐ ☐
111 I understand the net present value (NPV)
of a project
☐ ☐ ☐ ☐
111 I can complete an NPV (net present
value) calculation, using a calculator as
required
☐ ☐ ☐ ☐
QUESTION 7
A) Producing tally of the data set
8

B) Drawing histogram of the above data set
C) Comment on marks distribution
Average value of the marks = ∑FX / ∑F
= 1735 / 25
= 69.4
9

It can be said from the above data set and computation that, 7 students obtained average
marks which are such as 69.4 out of total 100.
Week 7
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do
111 I understand the idea of frequency
distribution
☐ ☐ ☐ ☐111 I can read and interpret a histogram ☐ ☐ ☐ ☐111 I can construct a histogram from a set of
data
☐ ☐ ☐ ☐
QUESTION 8
From the below table of self assessment it can be said that, I have not knowledge about
the probabilities and its calculation as well. Further, I cannot perform any kind of computation
and resolve equation of it. Therefore, simplification of provided data and equations are not done
and attempted by me.
Week 8
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t
do111 I understand simple probabilities ☐ ☐ ☐ ☐111 I can perform probability calculations,
using a calculator if required
☐ ☐ ☐ ☐111 I understand and can perform exchange
rate calculations
☐ ☐ ☐ ☐
10

SECTION 2
TASK 1: Two examples of real life
First illustration is relating to the NPV computation, when I was going to undertake a
new project at the workplace of my company. I21 had simultaneous three projects and by
calculating the NPV of them I able to know feasibility or viability of all the projects. Further, the
one specific project which has higher NPV that is undertaken by me which helps to generate
profitable return.
Apart from this, second example is regarding to the simple interest rate at the time of
making investment in the bank at particular interest rate. In this, the bank give lower amount of
the interest but by using calculation I am able to take the money which is really incurred. Due to
this, I not fall under the fraud of bank and take actual amount of the interest.
TASK 3: Reflective log
From the current study I have been found that, I am the well aware and knowledgable of
the power, interest rate, net present value, frequency distribution etc. Without taking any kind of
base and support I can easily make calculation of powers, simple as well as compound interest
etc. Further, in order to make computation of net present value (NPV) and prepare the frequency
distribution along with analysis I am highly confident. Therefore, any kind of support I not
required in this kind of calculations and performance.
It can be analysed from this study and analysis that, I have not any kind of knowledge
regarding to the linear equation as well as the probabilities. Due to such kind of reasons, I am not
able to perform any kind of calculation even they are very basic then also. Therefore, it is highly
necessary and needed to improve and enhance my knowledge about such both the items like
probabilities and linear equation. These will be supportive for me in order make effective
strategies and take fruitful decisions in my personal and professional or both life.
Experience of the numeracy 2 was excellent because of learning and getting different
kinds of new things and concepts. Before performing calculation of these questions or project I
aware about the indices and roots but not having idea about the various number of laws, which
11