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QTM511S - QUANTITATIVE METHODS - 2ND OPP - JULY 2023 |
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nAm I 8 IA unlVE RSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTYOF HEALTH,NATURALRESOURCESAND APPLIEDSCIENCES
SCHOOLOF NATURALAND APPLIEDSCIENCES
DEPARTMENTOF MATHEMATICS,STATISTICSAND ACTUARIALSCIENCE
QUALIFICATION: Bachelor of Technology: Accounting and Finance, Advanced Diploma in the
Theory of Accounting, Bachelor of Accountini; and Diploma in Accounting and Finance
QUALIFICATION CODE: 23BACF;07BACP;
06BDAF; 07 ADT A
LEVEL: 5
COURSECODE: QTMSllS
COURSENAME: QUANTITATIVE METHODS
SESSION:JULY 2023
DURATION: 3 HOURS
PAPER:THEORY
MARKS: 100
SUPPLEMENTARY/SECONDOPPORTUNITYEXAMINATION QUESTION PAPER
EXAMINER
Mrs. H.Y. Nkalle; Mrs. A. Sakaria; Dr. D. Ntirampeba; Mr. A. Mpugulu
MODERATOR:
Dr. D.B.GEMECHU
INSTRUCTIONS
I. Answer ALL the questions.
2. Write clearly and neatly.
3. Number the answers clearly.
PERMISSIBLEMATERIALS
I. Non-Programmable Calculator without the cover
ATTACHMENTS
2. Formula Sheet
THIS QUESTION PAPERCONSISTSOF 8 PAGES(Including this front page and formula sheet)
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Question 1 [2, 2, 3, 3, 2, 2 Marks]
Two thousand randomly selected adults were asked whether they have ever shopped on the internet.
The following table gives a two-way classification of the responses
Have
Have never
Shopped(H)
Shopped(N)
Male(M)
200
600
Female(F)
350
350
If one adult is selected at random from these 2000 adults, find the probability that this adult
9.1 Has never shopped on the internet
9.2 Is a male
9.3 Has shopped on the Internet given that this adult is a female
9.4 Is a male or has never shopped on the Internet?
9.5 Is a male or female
9.6 Are the events "female" and "have shopped" independent? Explain?
Question 2 [10, 2 Marks]
The table below shows the Database of ipod(s) sales and newspaper advertisements placed.
Advertisements (x)
Sales (y)
4
26
4
28
3
24
2
18
5
35
2
24
4
36
3
25
5
31
5
37
3
30
4
32
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2.1 Find the straight-line regression equation to estimate the number of ipods that are expected to be
sold based on the number of advertisement placed.
2.2 Predict the value of sales when number of advertisement is 6.
Question 3 [10 marks]
Given the prices (in N$) and per capita consumption (in N$) for apples, bananas, and oranges,
Determine the weighted price index using the Laspeyres method. Use 2010 as the base year. [10]
Year
2010
2014
Apple
p
0.692
0.896
Q
19.2
18.8
Banana
p
Q
0.342 20.2
0.491 31.4
Oranges
p
Q
0.365 14.3
0.843 8.6
Question 4 [11 marks]
-1
Let A= [
1
-1
1
-1] -1 . Solve the following homogeneous system of linear equations AX= 0 .Is the
-3
solution unique? Explain.
Question 5 [10 Marks]
Lama Abel borrowed N$20 000 at 5% for three and half years. She wants to pay N$8000 on maturity.
To achieve this, she is planning to pay 2000 in 10 months, 5000 in 16 months from now. How much
should she pay in two and half years from now to meet her obligation?
Question 6 [8 Marks]
Emma lpinge want to be able to withdraw N$8500 at the end of five years and withdraw N$3500 at the
end of seven years leaving a zero balance in the account after the last withdrawal. If she can earn a
simple interest of 6% p.a. on her balances, how much must she deposit in two years from now to satisfy
her withdrawal needs?
Question 7 [5 Marks]
A compound amount of N$ 2350 is due in 5 years. Determine the equivalent value of the debt in 2 years
from now, if money is worth 10% p.a. compounded twice a year.
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Question 8 [5 Marks]
Determine the time required to double the principal amount of $10, 000 invested in an account paying
interest at 5% compounded semi-annually.
Question 9 [11, 3 Marks]
A sum of N$100 has been deposited at the end of each month for the past 20 years into a special fund.
In the initial 10 years the fund is paying interest at 6% p.a compounded monthly. And in the last 10
years the fund is paying 12% interest p.a compounded monthly. Calculate the:
9.1 Total accumulated value of this annuity at the end of its 20-year term.
9.2 Compound interest earned by the annuity.
Question 10 [4 Marks]
Find the effective interest rate equivalent to a nominal rate of 15% compounded monthly.
Question 11 [2, 3, 2]
Define the following terminologies as applied in index numbers
11.1 Laspeyres Index
11.2 Index Number
11.3 Simple Index Number
41Page
End of paper
Total marks: 100
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Formula(s) sheet
I= prt
A= P(l + rt)
= - t
N-1
r
for
N>2
D =Adt
P = A(l - dt)
D=A-P
A= P(l + 2:.)mt
m
r=-- d
1-dt
reff
--
r
1-rt
SI Page
d=-r-
1+rt
= t logA-log:
m log (1+-m)
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= t
log2 r
mlog(l+m:)
paasche
=
"n ( Lt=l (Pi X
[L,i=l P1 X
qqo1))]
x
100
Laspeyers
=
"n ( Lt=1(P1X
[L,i=l Po X
qqoo))l
x
100
Laspeyers
=
[LL",int==l 1((PPoo
X
X
qqo1))]
x
100
2
Sx
=
-L-t=--1-
(xi -
n -1
x) 2
=
-L-t=--i -
x/
n-1
-
nx 2
"n 2
Sx=
L"1,in=lli F ( xi -
n-1
X-)2
=--L-,i-=-l-lixi
F2
n-1
-
nx-2
GI Page
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Mk =+Ij ~4(-kFn)
M=l
o
Mo + 2ffii--ffoo - h xh
=1 + fi-fo
Mo (Ii- fo) +(Ii- /;_)
n
Lfxi
X =-i=_l __
k
Lh
i=l
P(A n B)
P(B\\A) = P(A)
b=---nn-L-LXxY2 -
-
LXLY
(Lx) 2
n
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sx --vs]G
n
Bl Page