Calculating Compound Interest and Probabilities

This assignment focuses on the practical application of numeracy concepts. It involves calculating compound interest, understanding its relation to powers, and solving problems based on net present value. Additionally, it explores the use of numeracy in a real-life scenario – cricket, including probability calculations for tossing, recording runs, and measuring effectiveness using histograms and frequency tables.

Student Name
Student ID
Tutor
Portfolio Contents
1

Week / Content Section 1
Question
Learning Outcome Page
Section 1
1. Recap numeracy 1. Introduction, powers and use of
calculators
1 * 1,2
2. Powers, root, logarithms. Use of calculator 2 * 1,2
3. Simple & compound interest 3,4 * 1,2
4. Linear relationships. Scatter plots 5 * 1,2,3
5. Further linear relationships 5 * 1,2,3
6. The future value of money. Net present value. 6 * 1,2
7. Presentation of data. Histograms. 7 * 1,2,3
8. Probability. Exchange rates 8* 1,2
9. Revision None 1,2,3
Section 2
10. Real-Life Examples N/A 1,3
11. Online Activity N/A 1,2,3
12. Reflective Log N/A 1,2,3
* These sections are also being assessed via online quiz in section 2, Task 3
2

Section 1
You are required to complete this section immediately after completing the class sessions
related to each question.
Answer all questions and show your workings and/or explain your results.
Marks will be awarded for good presentation.
You may use your calculator as required.
You must show your workings.
QUESTION 1 [7 marks]
Powers and Roots:
a) State three Laws of indices and provide an example of each law (5 marks)
b) Simplify (1 mark)
c) Evaluate (1 mark)
[TYPE YOUR ANSWER HERE]
a) Indices is the way of representing the large numbers into short way. Three laws which can
represent indices in the better way are
Law 1: a^m * a^n = a^(m+n)
This is the first law which shows that when multiplying two identical numbers with
similar power, the final result will be same to the power of both exponents when they are
added together.
Example: 2^2 * 2^3 = 2^5
Law 2: a^m / a^n = a^(m-n)
Second law tells that when we divide two same numbers having different power, then
the power will be subtracted.
Example: 3^4 / 3^2 = 3^2
Law 3: (a^m)^n = a^(m*n)
The last and third law tells that if any number is having the power and that power is also
having the power, then to get the final result we have to multiply both the powers.
Example: (4^2)^3 = 4^6
b) 10^3 * 10^2
= (10)^5 = 100000
c) (5^3)^4 = 5^12 = 244140625
3

4

QUESTION 2 [7 marks]
a) Finding a root is the inverse of raising a number to a power
List three examples of root laws and explain what they are (5 marks)
b) Evaluate (1 mark)
c) Scientific notation is a special way to express very large or very small numbers and make
them easy to handle. Express 680,000 in a scientific notation (1 mark)
a) Square root is the function which takes any positive number as an input and return the
positive number in output, which would have been doubled or squared. The square root of any
number say x is denoted by
√ x
Example 1: if x ≥ 0 and y ≥ 0, the equation is
√ (x*y) = √a * √b
This only works in the multiplying factors.
Example 2: √ x^2 = I x I
√ (-2)^2 = I -2 I = 2
The square root will always give the positive number.
Example 3: if a ≥ 0, then √a^2 = a
√ 5^2 = 5
b) (1,000,000)^(1/6) = 10
c) scientific notation of 680,000 is = 6.8 * 10^5
[TYPE YOUR ANSWER TO QUESTION 2 HERE]
5

SKILLS AUDIT: WEEKS 1 – 2
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t do
1. I understand what a power of a number is ☐ ☐ ☐ ☐
2. I can perform calculations and
simplifications using indices
☐ ☐ ☐ ☐
3. I understand what a root of a number is ☐ ☐ ☐ ☐
4. I can perform calculations and
simplifications using roots, using a scientific
or financial calculator when required
☐ ☐ ☐ ☐
QUESTION 3 [10 marks]
Nelofa invests £50,000 at an interest rate of 3% per annum.
Calculate the final balance after 5 years:
a) Using the simple interest? (1 mark)
b) Using the interest compounded annually? (3 marks)
c) Using the interest compounded semi-annually? (3 marks)
d) Using the interest compounded quarterly? (3 marks)
[TYPE YOUR ANSWER TO QUESTION 3 HERE]
a) SI= P*R*T/100
where P = total amount occurred
A = capital amount
r = interest rate
t =given time period
therefore, A = 50,000*3*5/100
A = £7500
6

b) Compound interest annually = A = P[(1+r) n-1]
P =principle amount
r = rate of interest
t = total number of years
n = number of time interest is compound
= 50000 [(1+0.03)5-1]
= 50000*0.1592
= £7960
c) Compound interest semi-annually= P[(1+r/2) 2*n-1]
here, n=2
Therefore A = 50,000 [(1+0.03/2) 2*5-1]
= £8025
d) compound interest quarterly, then n = 4
therefore, A = 50,000 [(1+0.03/4) 4*5-1]
= £8060
7

QUESTION 4 [7 marks]
a) Jojoba invests £80,000 at a 4.5% interest rate annually.
Compounding the interest annually, how long will it take his investment
to double? (3
marks)
b) Roger deposits £8,000 in a bank savings account and after 10 years his balance is
£9751.96
Calculate the compound interest he received? Give your answer in three
significant figures. (4 marks)
[TYPE YOUR ANSWER TO QUESTION 4 HERE]
a) P0 = £80,000, r = 4.5%
Lets take P0 = initial investment
P = the amount after time t
r = interest rate
t = time
lets take x = initial investment (P0)
2x = final amount (P)= 1, 60, 000
C= P[(1+r)n]
160000= 80000 (1+0.04.5)n
= 15.8 years
It is therefore calculating the same by considering the rule of 72, it is expected to double in 16
years and will stand to 72/4.5
b) P0 = £8000
P = 9751.96
t = 10 years
We have to calculate interest rate first on the basis of given figures
P = P0(1+rt)
9751.96 = 8000(1+r*10)
9751.96/8000 = 1+10r
0.21 = 10r
r = 0.021
r = 2%
I) The compound interest received by roger annually i.e. n=1
A = p(1+r/n)^(rt)
A = 8000(1+0.021)^(10)
A = 8000(1.021)^10

A = £9847.95
II) The compound interest received by roger half yearly i.e. n=2
A = p(1+r/n)^(rt)
A = 8000(1+0.021/2)^(2*10)
A = £9858.62
III) Compound received quarterly i.e. n=4.
A = p(1+r/n)^(rt)
A = 8000(1+0.021/4)^(4*10)
A = £9864.00
WEEKS 3 – 4
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t do
5. I understand the idea of simple interest ☐ ☐ ☐ ☐
6. I can perform simple interest calculations ☐ ☐ ☐ ☐
7. I understand the idea of compound interest ☐ ☐ ☐ ☐
8. I can perform compound interest
calculations using a calculator if required
☐ ☐ ☐ ☐
9. I understand the Rule of 72 (or 69 or 70)
and can apply it in context.
☐ ☐ ☐ ☐
QUESTION 5 [9 marks]
a) Find the value of x if 5x – 15 = 45 (1 mark)
b) Solve the equation x + 20 = 0 (1 mark)
c) Solve the equation x-3/4 = 1 (2 marks)
d) Using y = 4x +2 (Do NOT draw graphs)
Complete the following table: (5 marks)
x = -2 -1 0 2 3 4
y = 4x + 2 = ? ? ? ? ? ?

[TYPE YOUR ANSWER TO QUESTION 5 HERE]
a) 5x – 15 = 45
5x = 45+15
x = 60/5
x = 12
b) if x+20 = 0, then
X = -20
c) x-3/4 = 1
x = 4+3
x = 7
d) y = 4x + 2
values of x = -2 -1 0 2 3 4
values of y = 4*-2 + 2 (4*-1+2) 4*0+2 4*2+2 4*3+2 4*4+2
values of x= -2 -1 0 2 3 4
values of y = -6 -2 2 10 14 18
WEEK 5

I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t do
10.I understand linear relationship between
two variables
☐ ☐ ☐ ☐
11.I can work out linear equation problems
given in this session
☐ ☐ ☐ ☐
12.I can plot a scatter graph from a set of data ☐ ☐ ☐ ☐
13.I understand the y-intercept and slope
(gradient) of a line graph and interpret their
meaning in real situations ().
☐ ☐ ☐ ☐
14.I can use scatter plot to derive a linear
relationship between two variables ().
☐ ☐ ☐ ☐
15.I am able to explain the use of scatter
graphs in business context
☐ ☐ ☐ ☐

Question 6 (10 marks)
ATOB Trading Ltd. is considering an investment project. The initial cost is £70,000. The annual
cash inflows (income) are projected to be as follows:
Year 1 Year 2 Year 3 Year 4
£14,000 £15,000 £25,000 £20,000
After 4 years the machine will be disposed of. The discount rate for this investment is 8% per
annum, compounded annually.
a) Work out the Net Present Value (NPV) of this investment. (8 marks)
b) Should ATOB Trading Ltd. proceed with this project?
Explain your reasoning. (2 mark)
[TYPE YOUR ANSWER TO QUESTION 6 HERE]
a) The net present value can be give as
NPV = -C0 +
(C1/1+r)+
(C2/(1+r)^2)+
(C3/(1+r)^3)+....
where
C = cash flow per year
C0 = initial investment
T = time
r = discount rate

NPV = - £9631
b) ATOB trading Ltd should not proceed with this project, because the net present value is
negative and the initial investment is high. Thus, there will be loss in the future, and the money
will be waste. So, they should not opt for this project.
WEEK 6
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t do
16.I understand the concept of the future
value of money
☐ ☐ ☐ ☐
17.I understand the net present value (NPV) of
a project
☐ ☐ ☐ ☐
18.I can complete an NPV (net present value)
calculation, using a calculator as required
☐ ☐ ☐ ☐
Question 7 (10 marks) (The material for this question is covered in week 8)
Below are results from a Numeracy 2 class test taken recently:
77 96 87 28 69
33 45 93 91 61
63 74 91 92 97
58 94 61 79 96
62 64 86 66 57
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)

[TYPE YOUR ANSWER TO QUESTION 7 HERE]
a)
77 96 87 28 69
33 45 93 91 61
63 74 91 92 97
58 94 61 79 96
62 64 86 66 57
The minimum value = 28
The maximum value = 97
Class Interval Tally marks Frequency
28-40 Ll 2
41-50 L 1
51-60 Ll 2
61-70 Llllll 7
71-80 Lll 3
81-90 Ll 2
91-100 Lllllll 8
This table shows the frequency and the interval of different class which will be helpful in
creating the histogram.
b) Histogram
Class Interval Frequency
28-40 2
41-50 1
51-60 2
61-70 7
71-80 3
81-90 2

91-100 8
c) The distribution of the marks is related to the time interval and frequency. The maximum
marks obtained are between 91-100, therefore their frequency is the highest. The lowest
frequency is for the class interval of 41-50.
WEEK 7
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t do
19.I understand the idea of frequency
distribution
☐ ☐ ☐ ☐
20.I can read and interpret a histogram ☐ ☐ ☐ ☐
21.I can construct a histogram from a set of
data
☐ ☐ ☐ ☐
Question 8 (10 marks)
28-40
41-50
51-60
61-70
71-80
81-90
91-100
012345678
Histogram

Assume a 5-sided spinner is spun giving the following results. The spinner is biased. The
probability that the spinner will land on number 1 is equal to the probability that it will land on
4.
N u m b e r s: 1 2 3 4 5
Probability : X 0.20 0.10 X 0.30
a) Give 4 real-life examples in which the basic probabilities are used? (1 mark)
b) Work out the value of x (3 marks)
c) Mark will spin the same 5-sided spinner 100 times. Estimate the number of times it is likely
to land on number 4. (2 marks)
d) List 4 examples of things said to have symmetry characteristics in a probability context
(4 marks)
[TYPE YOUR ANSWER TO QUESTION 8 HERE]
a) real life examples in which probabilities used are;
I) Games and recreational activities
II) sports strategies
III) weather reports
IV) Insurance operations
b) The spinner is having equal chances of landing on number 1 and on number 4, therefore the
value of x = 0.20
c) the spinner is having five sides, so each side will be having the probability of 1/100 to get the
chance. The probability of getting the number 4 = 20/100 = 0.2%
d) Examples of similar probability distribution
i) Spinner having infinite ends
ii) rain drops falling on a ruler
iii) the analogue to digital conversion
iv) Person waiting for the bus

WEEK 8
I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t do
22.I understand simple probabilities ☐ ☐ ☐ ☐
23.I can perform probability calculations, using
a calculator if required
☐ ☐ ☐ ☐
24.I understand and can perform exchange
rate calculations
☐ ☐ ☐ ☐

Module Code Module Title Summer 2017 Coursework Brief
Section 2
Task 1 - Two Real life examples (100 words each)
Give two real-life examples 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)).
[TYPE YOUR ANSWERS TO TASK 1 HERE]
(I) The main example based on the numeracy that has been experienced by me when I
sold my old car and took a loan in order to buy a new car. In order to understand the
complex calculation of the amount that I had to pay in form of instalments of that loan,
it is essential to possess ability to solve problems based on Simple interest and
compound interest so that the amount that has to be pay can be evaluated. Although, I
found that simple interest is easy to calculate whereas compound interest is a little
tough from the calculation's point of view. In addition to this, calculation of compound
interest also involves the knowledge of powers. Further, when I sold my old car I have
to solve problems based on Net present value.
(ii) Importance of numeracy in daily life is also experienced by me during the school
time when I used to play cricket. Although, it sounds like just a sport but in actual
terms there are some calculations needed in this. For example, use of probability when
tossing for batting and bowling. Also, I recorded runs scored by me in individual match
and measured by effectiveness suing histogram and frequency tables. In addition to
this, I also checked my average by calculating mean of scores of individual matches.
Task 2 - Online Activity
This section covers the online quiz. You must complete and pass all 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%
[PASTE YOUR SCREENSHOT FOR TASK 2 HERE]
Task 3 - Reflective Log (150 words)

Module Code Module Title Summer 2017 Coursework Brief
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 probabilities, I need to practice more or
research etc.)”
 How would you evaluate your experience of Numeracy 2 module (e.g. contribution to
classes, independent study etc.)
[TYPE YOUR ANSWER TO TASK 3 HERE]
The most confident topic for me was power roots, interest rates was also good but the
functions of power and roots are easy to understand and solve. The calculation done in
this module related to roots and power were easy and I was able to complete those
practices in the given time frame. Week 7 was time consuming because the
development of histogram was a little difficult. Rest all the things were done very
smoothly.
The major area of improvement required was in probability, as it was not
understood to me very clearly. I was giving full attention in my classes, so it was very
helpful. The practices of each week helped me a lot in understanding the Numeracy
module. I have done independent study as well, so that I will understand the topic
more easily and can apply those practices while solving the given problems. Overall the
experience was very good.