MAII3007 Numeracy 2: Comprehensive Portfolio Assignment Spring 2018

This document presents a complete solution to a Numeracy 2 (MAII3007) portfolio assignment, covering topics such as laws of indices, scientific notation, simple and compound interest calculations, net present value (NPV), frequency distribution, histograms, and probability. The assignment includes detailed solutions to mathematical problems, skills audits reflecting on the student's understanding of key concepts, and a discussion on the application of these concepts. The student expresses confidence in areas like compound interest and NPV, while acknowledging the need for further practice in probability. The document also features screenshots of online activities completed as part of the module.

NUMERACY 2 (MAII3007) Re-sit Portfolio
Assignment
Student Name and id
[Pick the date]
Section 1

Question 1
a) The two laws of indices are highlighted below:
1. Any number rather than zero whose index is zero would always be equal to 1, irrespective of
the value of the base.
a0=1
1000 =1
2. When two or more expressions with the same base are taken to do multiplication than the
solution of this would be the sum of indices of the base.
am × an=am+n
52 ×53=52+3=3125
b) 35 ×33
¿ ( 3 )5 +3
¿ 38
¿ 6561
c) (10¿¿ 3)2 ¿
¿( 10)3 × 2
¿( 10)6
¿ 1,000,000
d) 185 ×184
¿ 18 (5 +4 )
¿ 189
1

¿ 1.983 ×1011
Question 2
a) The requisite examples are as indicated below.
√2 = 21/2
√8 = 23/2
b) 3
√729
¿( 729)
1
3
¿( 9∗9∗9)
1
3
¿((9)¿¿ 3)
1
3 ¿
¿ 91
¿ 9
c) Scientific notation
Number = 9,876,567
Scientific notation = 9.876567 ×106
SKILLS AUDIT: WEEKS 1 – 2 (Taught in week 3)
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 or powers.
☒ ☐ ☐ ☐
2

3. I understand what a root of a number is. ☐ ☒ ☐ ☐
4. I can perform calculations and
simplifications using roots and using a
scientific with a calculator.
☒ ☐ ☐ ☐
Question 3
P=£ 120,000
i=4.5 % p . a.
n=5 year
a) By simple interest
I =P∗i∗n
I = 120,000∗4.5
100 ∗5
I=£ 27,000
Total final amount at the end of 5 year A = I +P = £ 120,000+£ 27,000=£ 147,000
b) By interest compounded annually
A=P ( 1+r )n
A=120,000∗( 1+0.045 )(5)
A=£ 149,541.8
c) By interest compounded semi-annually
A=P (1+ r
n )nt
A=120,000∗(1+ 0.045
2 )(5∗2 )
3

A=£ 149,904.41
d) By interest compounded quarterly
A=P (1+ r
n )nt
A=120,000∗(1+ 0.045
4 )(5∗4)
A=£ 150,090.1
Question 4
a. Grace has invested = £ 250,000
Interest rate annually = 6.5%
Compounding interest annually
Time when the investment would double
A=P ( 1+r )n
2∗250000=250000(1+0.065)n
2 ¿(1+0.065)n
log 2=n log ( 1.065 )
n= log 2
log ( 1.065 ) = 0.30102
0.02734
n=11.00674
Therefore, 11 years would be required for the investment to get doubled.
b. Hussein has deposited = £ 11,077
Compound interest rate =?
Time = 10 years
4

Final balance after 10 years =£ 15 , 647.50
A=P ( 1+r )n
15,647.50=11,077 (1+i)10
15,647.50
11,077 =(1+i )10
1.4126=(1+i)10
(1.4126)
1
10 =(1+i)
1.0351=1+i
i=0.03514∨3.51 %
Therefore, requisite interest amount would be 3.51% annually.
WEEKS 3 – 4 (Taught in week 3)
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
a) x=?
5 x−105=300
5

5 x=300+105
x= 405
5
x=81
b) x +81=505
x +81−81=505−81
x=424
c) x=?
4 x−2
4 =12
4 x−2=12∗4
4 x−2=48
4 x=48+ 2
4 x=50
x= 50
4
x=12.5
d) y=12.5 x +2
WEEK 5 (Taught in week 4)
6

I know how to…. I can do
well
I need
practice
I’m not
sure
I can’t do
10. I understand the concept of a linear
relationship between two variables.
☒ ☐ ☐ ☐
11. I can work out the linear equation given in
this portfolio.
☒ ☐ ☐ ☐
12. I can draw a scatter plot from a set of data
and apply a line of best fit.
☒ ☐ ☐ ☐
13. I understand the y-intercept and slope
(gradient) of a line graph and interpret their
meaning to real-life situations ( y=mx+c).
☒ ☐ ☐ ☐
14. I can use a scatter plot to derive a linear
relationship between two variables (
y=mx+c).
☒ ☐ ☐ ☐
15. I am able to explain the use of scatter
graphs in a business context.
☒ ☐ ☐ ☐
Question 6
Initial cost = £700,000
n=4 year
Discount rate i=10 % p . a .(compounded annually)
a. Net present value NPV
Case outflow ¿−£ 700,000
Cash inflows = 125,000
(1.10)0 + 145,000
(1.10)1 + 270,000
( 1.10)2 +386,000
(1.10)3 =£ 1894966
Net present value NPV = Case outflow+ Cash inflows
NPV =−£ 700,000+ £ 1894966=+ £ 1,194,966
7

b) Since NPV of the project has come out to be positive as computed above, hence Jedediah Ltd
should proceed with the project.
WEEK 6 (Taught in week 5)
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 calculation, using a
calculator as required.
☒ ☐ ☐ ☐
Question 7
a) Tally of the above shown class test scores is shown below:
Data Tally
20-29 ||||
30-39 ||
40-49 ||||
50-59 |||| |
60-69 |||
70-79 ||||
80-90 |
Grand Total 25
b) The histogram for the test scores is indicated below.
8

c) It is apparent that the given distribution of marks is not normal. This is apparent from the
above histogram which is asymmetric and hence no symmetric in shape. Further, there is a
presence of positive skew or a tail on the right.
WEEK 7 (Taught in week 6)
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
a) Number of male student = 22
Number of female student =18
9

Probability that randomly selected student would be a female =?
Favourable case = 18
Total cases = 18 +22 = 40
Probability that randomly selected student would be a female =18/40= 0.45
b) Probability of rainfall in next day = 40% or 0.40
Probability of no rainfall in next day = 1- 0.40 = 0.60
c) (b) 1.02 and (d) 101% are not the probabilities. This is because probability cannot be higher
than 1.
d) Number of blue balls =5
Number of red balls =7
Number of yellow balls =8
Probability that a randomly selected ball is yellow = 8/20 = 0.40
Probability that a randomly selected ball is not yellow = 1-0.40 = 0.60
WEEK 8 (Taught in week 7)
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.
☒ ☐ ☐ ☐
10

Section 2
Task 1
1) Suppose a bank representative approaches me and offers four different types of account
namely A,B,C and D. The annual interest rate for each of these accounts is 6% p.a. However,
the difference between these accounts is the compounding frequency which for A,B,C,D is
monthly, quarterly, semi-annually and annual. The bank representative asks me to choose an
account.
For the given problem, I should choose account A as it takes the least amount of days for
compounding and hence after a year, the same amount of principal would result in the highest
amount for account A since the money would be compounded 12 times a year. However, for
the other accounts, the amount of compounding done in an year would be lesser yielding
lower effective annual rate.
2) Consider a situation in which a friend owes me $ 10,000 but instead of paying that amount at
one go, he proposes that he would pay this amount in equal annual instalments of $ 2,200
each. Assume that a risk free interest of 10% p.a. can be earned. So the question is if I should
accept this proposal or instead demand full immediate payment of $ 10,000.
In order to resolve the given situation, we would compute the NPV of the above proposal. The
NPV of this proposal is computed below.
NPV = -10000 + 2200/1.1 + 2200/1.12 + 2200/1.13 + 2200/1.14 + 2200/1.15 = -$1,660
Since the NPV of the proposal is negative, hence I should not accept this offer and instead
demand immediate payment of $10,000.
Task 2
The requisite screenshots for the online activities are as highlighted below.
11

Task 3
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I feel confident about a host of topics ranging from compound interest, simple interest, powers,
roots along with NPV. This is primarily because my basic understanding of these topics is quite
exhaustive and also I have also solved enough questions on these topics thus enhancing my
confidence level. However, there are certain topics especially probability which are still not very
clear especially with regards to application in relatively complex problems. Thus, more practice
would be helpful for these concepts.
The overall experience of the Numeracy 2 module was quite enriching particularly because of
the overall learning that was derived in the module. In particular, there was rich peer to peer
learning which enabled me to clarify the various concepts which have haunted me since my days
in primary education. Besides, the faculty was quite helpful in clarifying the concepts along with
various doubts that I had about the key topics covered. Additionally, the knowledge about the
concepts covered in the module would be immensely helpful in my future life.
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