Business Numeracy Assignment: Indices, Interest, Probability, and NPV

This document presents a comprehensive solution to a numeracy assignment, covering a range of fundamental mathematical concepts relevant to business and finance. The assignment delves into the laws of indices, simplifying expressions, and evaluating their values. It explores root laws and their ...Read More

NUMERACY

TABLE OF CONTENTS
QUESTION 1...................................................................................................................................1
A. Three Laws of Indices............................................................................................................1
B. Simplification.........................................................................................................................1
C. Evaluation...............................................................................................................................2
QUESTION 2...................................................................................................................................2
A. Root Laws and Examples.......................................................................................................2
B. Evaluation...............................................................................................................................3
C. Expression in a scientific notation..........................................................................................3
QUESTION 3...................................................................................................................................3
A. Final balance using the simple interest..................................................................................3
QUESTION 4...................................................................................................................................4
A. While compounding the interest annually, time taken to double the investment..................4
B. Calculating the compound Interest ........................................................................................4
QUESTION 5...................................................................................................................................4
A. Finding the value of x.............................................................................................................4
QUESTION 6...................................................................................................................................5
A. Net Present Value (NPV) of the investment..........................................................................5
B. Reasoning for proceeding the process in ATOP Trading Ltd. ..............................................6
QUESTION 7...................................................................................................................................6
A. Tally for the given data..........................................................................................................6
B. Histogram of the data set........................................................................................................6
C. Ideas on the distribution of the marks....................................................................................7
QUESTION 8...................................................................................................................................7
A. Real life examples of Probability...........................................................................................7
B. Value for x..............................................................................................................................7
C. Estimation of the number that it lands on number 4..............................................................7
D. Characteristics similar to the probability context...................................................................8
SECTION 2......................................................................................................................................8
TASK 1............................................................................................................................................8

TASK 3............................................................................................................................................8

QUESTION 1
A. Three Laws of Indices
For writing a product of numbers shortly, a power or index is used. The plural of that
index is indices. All the three laws are discussed below :
First Law
It states that when the expressions with the same bases are being multiplied, the powers or
indices are added.
am * an = am+n
e.g. We can take the following example
76 * 74 = 76+4 = 710
In the example above, it is clear that the both the bases are same as 7, so powers are added.
Second Law
It states that when the same bases are being divided, the powers or indices are being subtracted.
am/an = am-n
Here, we can take the following example
85/83 = 85-3 = 82
Third Law
It states that to reach an expression of an nth index, copy the base and multiply the indices.
(am)n = amn
In this, we can take the following example,
(64)2 = 64*2 =68
B. Simplification
In case of first law,
am * an = 76 * 74
am+n = 76+4
= 710
In case of second law,
am/an = 85/83
1

am+n = 85-3
= 82
In case of third law,
(am)n = (64)2
amn = 64*2
=68
C. Evaluation
As in case of First Law, it says if bases are same, powers are added.
Simplifying on the basis of the example explained above,
The law explains am * an = am+n
and the example, 76 * 74 = 76+4 = 710
As base is 7 and powers/indices are 6 and 4, so both the indices will be added as the bases are
same. Hence, in getting the results.
As in case of Second Law, it says that if both the bases are same and are divided, the indices will
be subtracted. The law explains am/an = am-n
The example is 85/83 = 85-3 = 82
As the bases are same as 8, both the indices i.e. 5 and 3 are being subtracted, hence giving the
results.
In case of Third Law,
The law explains (am)n = amn
The example is 76 * 74 = 76+4 = 710
In this, to get an expression or result of the nth index, copying the bas with the indices will help
in getting the results. Base is given as 7 and the indices are 6 and 4, therefore resulting in
addition of both the indices, hence giving the results.
QUESTION 2
A. Root Laws and Examples
First law
b = √a if both b>=0 and b2 = a
Here, we can take the following example,
2

√9 = 3 as 32= 9
Second Law
√a2 = |a|
Example,
√(-5)2 = |-5| = 5
Third Law
If a>=0 then, √a2 = a
Here, we can take the following example
√122 = 12
B. Evaluation
In case of First Law,
b = √a if and only if both the following factors b>=0 and b2 = a implies true.
In case of Second Law,
√a2 = |a|
The square root of a is equal to the determinant of a.
In case of Third Law,
it states if a>=0,
then √a2 = a
It means if a is equal to zero or any value more than 0, the square root of a will be equal to a
itself.
C. Expression in a scientific notation
The Decimal notation given is 680,000
After converting it in Scientific notation, the result will be 6.8 * 102
QUESTION 3
A. Final balance using the simple interest
Nelofa invested 50,000$ at an interest rate of 3% per annum,
The final balance after 5 years will be as following :
1. Using Simple interest
Principle or Sum (P) = 50,000$
Rate % per annum [R] = 3%
3

Time = 5 years
therefore, S.I i.e. Simple interest = 7500.
2.Using Compound Interest annually
Principle or Sum (P) = 50,000$
Rate % per annum [R] = 3%
Time = 5 years
Therefore, Compound Interest (C.I) = 7963.70
3. Using Compound Interest semi annually
Principle or Sum (P) = 50,000$
Rate % per annum [R] = 3%
Time = 5 years
Therefore, Compound Interest (C.I) = 8027.04
4. Using Compound Interest quarterly
Principle or Sum (P) = 50,000$
Rate % per annum [R] = 3%
Time = 5 years
Therefore, Compound Interest (C.I) = 8059.21
QUESTION 4
A. While compounding the interest annually, time taken to double the investment
As per Rule of 72,
Base Amount = 80000£
Annual Interest Rate = 4.5%
Calculation Period = 16 years ( as according to rule of 72, 72/4.5=16 years)
The resulted balance after compounding the interest annually will be £164,133.48
B. Calculating the compound Interest
Here, we have to check the compound interest Roger will receive :
9751 = 8000(1+r/100)10
9751/8000= (1+r/100)10
1.218 = (1 + r/100)10
(1.218)1/10 = 1 + r/100
4

= 6.622= 1 + r/100
r = 5.622/100
= 0.0562
QUESTION 5
A. Finding the value of x
a)The value of x is x+ 20= 0; x= -20
b) x is given various values. Now, we calculate the value of it by the following steps :
x + 20= 0
therefore, x= -20.
c) if x + 20 = 1
x = 1 – 20
= -19
d) Given y = 4x + 2
x has given various values, evaluating the value of y for each
when x = -2, y= -6
x = -1, y= -2
x = 0, y= 2
x = 2, y= 10
x= 3, y= 14
x=4, y=18
QUESTION 6
A. Net Present Value (NPV) of the investment
Initial investment = 70000£
Discount Rate = 8%
Cash Flow per year :
Year 1 = 14000£
Year 2 = 15000
Year 3 = 25000
5

Year 4 = 20000
Now, we have to calculate the NPV value :
NPV = -C0 + C1/1+r + C2/(1+r)2 +........Cr/(1+r)T
= - 9,630.55 £
B. Reasoning for proceeding the process in ATOP Trading Ltd.
Yes, the company must proceed with the project as we have got a negative value as a
resultant. It means the investment producing a high discount rate. Therefore, it means the present
cost value will exceed the present revenue value.
QUESTION 7
A. Tally for the given data
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B. Histogram of the data set
C. Ideas on the distribution of the marks
The more number of students have failed in the category of 60-65. In the category of 85-
90, 90-95 and 95-100 also a large number of students have failed. IN the class interval of 35-40,
40-45, 50-55 and from 80-85, none has failed.
QUESTION 8
A. Real life examples of Probability
1. Planning over the weather.
2. Sportsmen often determines the best games strategies.
3. An analyse of insurance policies for which plans are best.
4. In various recreational activities like to play cards or to play video games etc.
B. Value for x
Numbers 1 2 3 4 5
Probability x 0.20 0.10 x 0.30
7

The whole sum of probability comes as 0.6
The probability for every thing comes as 1, therefore 1-0.60 = 0.4/2 = 0.2= x
C. Estimation of the number that it lands on number 4
As Mark has spin the spinner for about 100 times, we have to estimate the number of
times it is likely to land on number 4.
At 4, we were having the probability of 0.2 , so 0.2 *100 = 20 times.
Therefore, for about 20 times, the ball is likely to be land on number 4.
D. Characteristics similar to the probability context
Very often when people went on a walk, they observe the weather conditions. According
to the climate of that day, they start observing the whole day climate. It represents that there are
some factors that are similar to the context of probability. Like this way, there are various other
factors also like the sportsmen often look for strategies or methods while playing. They actually
estimates it on some basis. This factor also is similar to the context of probability.
SECTION 2
TASK 1
NPV can help solving various problems in business. As we can consider an asset that
produces the same amount for the income every year, that starts producing a different amount
every year. Also, if it is generating the income from now to eternity, the asset if can produce a
stream of income over some particular period of time. It may be for 5, 10 or may be 50 years.
TASK 3
Although all the topics including powers and roots, interest rates are very much effective
but I think NPV proves much more effective and better than the others. While evaluating the
Numeracy module 2, I felt attending properly the classes play a very important role. It helps the
individuals to stay in touch with the work going on. Self study can also be a better idea. It helps
in developing the self concentration level and the person can focus more better.
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