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QTM511S - QUANTITATIVE METHODS - 1ST OPP - JUNE 2022 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
Faculty of Health, Applied Sciences &Natural Resources
Department of Mathematics and Statistics
QUALIFICATION : Bachelor of Technology : Accounting and Finance, Advanced Diploma in the
Theory of Accounting, Bachelor of Accounting and Diploma in Accounting and Finance
QUALIFICATION CODE: 23BACF ;07BACP;
O6BDAF; O7ADTA
LEVEL: 5
COURSE: QUANTITATIVE METHODS
COURSE CODE: QTM511S
SESSION: June 2022
DURATION: 3 Hours
PAPER: THEORY
MARKS: 100
EXAMINER(S)
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
Mrs. H.Y. Nkalle; Mrs. A. Sakaria; Dr. J. Ongala; Dr. D. Ntirampeba; Prof. A.S.
Eegunjobi
MODERATOR: Dr. D.B. Gemechu
INSTRUCTIONS
1. Answer ALL the questions.
2. Write clearly and neatly.
3. Number the answers clearly.
PERMISSIBLE MATERIALS
1. Non-Programmable Calculator without the cover
ATTACHMENTS
2. Formula Sheet
THIS QUESTION PAPER CONSISTS OF 5 PAGES (Including this front page)
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Question 1
If Yvonne lends N$4500 to Golda at 10% p.a. and Golda lends the same sum to Tida at 11.5% p.a., then
the gain of Golda in a period of 4 years is?
[5]
Question 2
Mr. Nkalle invested an amount of NS20,900 divided in two different schemes A and B at the simple
interest rate of 9% p.a. and 8% p.a, respectively. If the total amount of simple interest earned in 2 years
is NS3508, what was the amount invested in Scheme B?
[8]
Question 3
If you start a bank account with N$15,000 and your bank compounds the interest monthly at
an interest rate of 9% p.a, how much money do you have at the year's end?
(Assume that you do not add or withdraw any money to/from the account).
[5]
Question 4
Milly took a loan of N$900 with simple interest for as many years as the rate of interest. If she paid
N$324 as interest at the end of the loan period, what was the rate of interest?
[5]
Question 5
N$1000 is placed in an account at 4% compounded annually for 2 years. It is then withdrawn at the end
of the two years and placed in another bank at the rate of 5% compounded semi annually for 4 years.
What is the balance in the second account after the 4 years?
[7]
Question 6
If Jacob takes out a discounted loan with a face value of NS 5000 for 6 months from a lender who
charges a 9.5% discount rate, what is the discount, and how much money does Jacob receive? [6]
Question 7
A machine costing N$200 000 has effective life of 7 years and its scrap value is NS30000. What amount
should the company deposit annually into a sinking fund earning 5% per annum so that it can replace
the machine after its useful life? Assume that a new machine will cost NS300 000 after 7 years. [7]
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Question 8
Find the effective interest rate equivalent to a nominal rate of 10% compounded monthly. [5]
Question 9
9.1 Nam Water recently surveyed a sample of employees to determine how far they lived from their
corporate headquarters. The results are shown below.
Distance (in Km)
Oupto5
5 up to 10
10 up to 15
15 up to 20
20 up to 25
Number of days
4
15
27
18
6
9.1.1 Compute and interpret the modal distance.
[6]
9.1.2 Find the minimum distance associated with the 25% of employees living further away from
Nam Water headquarter.
[5]
9.1.3 Compute the interquartile range.
[7]
Question 10
A used cars spare parts company that specialises in imported cars has recorded its ordered and cost of
screens for its three different screes. The screens are classified as Front, side, and rear.
Cartridge
Front
Side
Rear
2015
Unit price
(NS)
4500
2450
6500
Quantity
ordered
24
37
12
2017
Unity price | Quantity
ordered
6500
36
4600
44
7850
14
10.1. Construct a quantity index to reflect the overall change in quantities of screens ordered for the
period 2015 — 2017. Use the Paasche approach. Interpret your index.
[5]
10.2. Calculate the unweighted aggregate price index for 2017 on 2015 as base year. Interpret your
index.
[4]
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Question 11
The quarterly visitors of a large tourist site have been recorded for four years. These data are listed
here
Year
1999
2000
2001
2002
Quarter
Winter
Spring
Summer
Fall
Winter
Spring
Summer
Fall
Winter
Spring
Summer
Fall
Winter
Spring
Summer
Fall
Visitors (in 1000)
117
80.7
129.6
76.1
118.6
82.5
121.4
77.0
114
84.3
119.9
75.0
120.7
79.6
130.7
69.6
Compute the 4-period centered moving average for the quarterly visitors.
[4]
Question 12
Solve the following inequality
6x3-4.3 ,
[3]
Question 13
13.1. Researchers at Namibia University of Science and Technology (NUST) have determined that
children under 2 years old who sleep with the light on have a 36 % chance of becoming myopic before
they are 16. Children who sleep in darkness have a 21 % chance of becoming myopic. A survey indicated
that 28% of children under 2 sleeps with some light on. Find the probability that child under 16 is
myopic.
[4]
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13.2. What is the term used to describe two events whose union is the same as the sample space? [2]
Question 14
Define the following terminologies as applied in index numbers
14.1 Laspeyres Index
[2]
14.2 Index Number
[3]
14.3 Simple Index Number
[2]
End of exam paper
Total marks: 100
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Formula(s) sheet
[= prt
A= P(1+7t)
t=" forN>2
D = Adt
P = A(1 —dt)
D=A-P
A=_P(1+=)lymt
r=—1-—ddt
-
"eff ~ Tort
_ 9T
1+rt
__ logA-logP
— m log (+7T)r
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log2
~ mlog(1+—)
n= RE 1+i)"-1
dy = RO1-(1+i)~™”
paasche = Fteee x
x 100
i=1(Po x q1)
paasche = F dizteio (P1eXx Io) x 100
Laspeyers = Fe te e x
x 100
i=1(Po X Yo)
Laspeyers
=
fetie=n1(ePo
x
X
aqo)
x 100
gx2—= ina (%; — X)? _ die1 Xi” — Nx?
n—1
n-1
i = tat fii — Z_)*
*
n—-1
jaa fixi Z — nx—?_
n—-1
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M,=1+4f(\\4"7 |
M, = ly "A2hcfho- tr yp
MG fHAah fy
P(B\\A)
=
P(ANB)
P(A)
b
_nyxy-dUxdy
ny x* — (yx)?
uy-byx
n
b _=5x2y
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CV =—Sxx 100
xX