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QTM511S - QUANTITATIVE METHOODS - 2ND OPP - JANUARY 2025 |
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r
nAm I BIA UnlVERSITY
OF SCIEnCEAnDTECHnOLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoolof NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
13JacksonKaujeuaStreet
Private Bag 13388
Windhoek
NAMIBIA
T: •264 61207 2913
E: msas@nust.na
W: www.nust.na
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, 06BDAF, 07ADTA NQF LEVEL:5
COURSE: QUANTITATIVE METHODS
COURSE CODE: QTMSllS
DATE: JANUARY 2025
SESSION: 2
DURATION: 3 HOURS
MARKS: 100
SECOND OPPORTUNITY/ SUPPLEMENTARY: EXAMINATION QUESTION PAPER
EXAMINER:
MODERATOR:
Mr. Akser L Mpugulu
Dr Dibaba Gemechu
INSTRUCTIONS:
1. There are 5 questions
2. Answer ALL questions on the separate answer sheet.
3. Please write neatly and legibly.
4. Do not use the left side margin of the exam paper. This must be allowed for the
examiner.
5. All written work must be done in blue or black ink and sketches must be done in
pencil.
6. Number all answers clearly and show clearly all the steps used in the calculations.
PERMISSIBLE MATERIALS:
Non-Programmable Calculator without a cover.
This question paper consists of 6 pages including this front page.
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1. Question 1:
[20 Marks]
1.1. A principal of N$5000 is invested at a simple interest rate of 7% per annum. How
long will it take for the principal to triple in value?
(5)
1.2. A loan of N$5,000 is due in 18 months, with a 6.5% interest rate. If the loan is repaid
6 months earlier than the due date, calculate the value of the debt.
(6)
1.3. On February 5, a company signed a N$75,000 note with a simple interest rate of 11%
for 180 days. The company made payments of N$15,000 on April 12 and N$20,000
on June 20. How much will the company owe on the maturity date? (Use the USA
rule).
(9)
2. Question 2:
[21 Marks]
2.1. Dr. Amunjela invested N$40,000 in two different schemes, X and Y. Scheme X
offers a simple interest rate of 9% p.a., and Scheme Y offers a rate of 5% p.a. The
total simple interest earned in 4 years is N$10,800. How much was invested in
Scheme X?
(7)
2.2. An investor makes monthly payments of N$1,000 into an account that earns 6%
interest per annum, compounded monthly, for 5 years.
2.2.1. Calculate the future value of this ordinary annuity.
(4)
2.2.2. Explain how would the future value change, If the payments were made at the
beginning of each month.
(2)
2.3. A business owner takes out a loan of N$100,000, to be repaid over 10 years at an
interest rate of 7% per annum, compounded monthly.
2.3.1. Calculate the monthly repayment amount.
(4)
2.3.2. How much of the first payment goes toward interest.
(2)
2.3.3. What is the total amount repaid over the 10 years.
(1)
2.3.4. How much interest paid?
(1)
3. Question 3:
3.1. Consider the linear system of equations:
QUANTITATIVE METHODS
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[14 Marks]
2NDOPPORTUNITY
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X + 2y + Z = 0
2x + 4y + 3z = 0
-x - 2y- 2z = 0
3.1.1. Construct the augmented matrix and reduce it to row echelon form.
(6)
3.1.2. Discuss the implications of your row reduction results regarding the existence of
solutions.
(2)
3.2. Solve the following inequality:
3.2.1.
zx < < zx-4
x+S - 3 - 3x
4. Question 4:
(6)
[12 Marks]
4.1. An investor has a portfolio of real estate properties. The prices and square footage
owned in 2015 and 2020 are shown below:
Property
X
y
z
2015 Price
(N$)
300,000
500,000
450,000
2015 Area
(mz)
1,000
1,200
900
2020 Price
(N$)
350,000
550,000
480,000
2020 Area
(mz)
950
1,100
1,000
4.1.1. Calculate the Paasche Price Index for the real estate portfolio using the weighted
aggregate method.
(7)
4.1.2. Calculate the Laspeyres Quantity Index for the real estate portfolio using the
weighted aggregate method.
(5)
5. Question 5:
[33 Marks]
5.1. A restaurant recorded the dining times (in hours) of 80 customers. The frequency
distribution is as follows:
Time Interval (hours)
0.5-< 1.0
1.0-< 1.5
1.5-<2.0
2.0-<2.5
2.5-< 3.0
Number of Customers
15
25
20
12
8
5.1.1. Calculate the estimated average dining time for a customer.
(8)
5.1.2. Calculate the modal dinning time.
(5)
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5.2. The number of units sold for a product over a span of eleven years is recorded. The
data is as follows:
Year
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Units Sold
(1,000)
245
290
303
275
265
281
316
282
272
295
327
5.2.1. Determine the least squares trend line equation for the above dataset. Use the
sequential coding method.
Hint: start your coding by assigning 1 for the first time period.
(11)
5.2.2. Predict the trend value for the sales of the product for 2017.
(3)
5.3. In a local election, 55% of eligible voters are aware of the candidate's campaign. The
probability that an aware voter will vote is 80%, while the probability that an
unaware voter will vote is 40%.
5.3.1. What is the probability that a randomly chosen voter will vote?
(3)
5.3.2. What is the probability that a voter was aware of the campaign, given that they
voted?
(3)
END OF QUESTION PAPER
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2ND OPPORTUNITY
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SUMMARY OF FORMULAE QTM511S: 2024
Simple Interest:
Discount:
Compound Interest:
Simple discount Rate:
Effective Interest Rate:
Effective Interest Rate:
I =Prt
P=A(l-dt),
A= P(l+rt)
D=Adt
+:Ill/
A= P ( 1
)
d
r
1 + rt
r
elf
----1-r rt
I+: = refl
(
Ill
) -1
Nominal Interest Rate:
Annuity:
Sn =R
r
m
s f---- ;;-J;
1-+(!1:._)-l7
= A R ___ 11_-1
17
r
m
lo(gI+;)' log(!+:) Period: t = _l_o_g_S_-_lo_g_P_ n=-___,,1.o__g2_
m
t=--Nfo-r1
r
N>2
log(- iS 11 + I)
n=------ R
log(l + i)
Measures of Central Tendency
log(l- -iA11 )
n=-'-
R
log(l + i)
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Mean
Median
Mode
+h[ M =l
0 Mo
2J;J_;-lfoo_h ] '
Measures of dispersion
I {' I( Variance=
;;X- ? -n (X-)2
11
or
X;-X )'
Variance = ---'-----'--
n-1
n- I
Standard
variance ,
Quartile
)x coefficient of variation =( I01
Index Numbers
f Laspeyres price index = ip, x % x I00%
·
Po X qo
I(Pi xq,)
Paasche price index= """'(
) x 100%
Pox q,
f iPo i Laspeyres quantity index -
x q, x I00%
Po xq"
f i i Paasche quantity ;ndex - P, x qI x I00%
P1X%
Time Series
y=a+bx
n
Probability
P(AuB)=P(A)+P(B)-P(AnB) P(AnB)=P(A)P(B)
PB(A-I
)
_P(AnB)
P(A)
QUANTITATIVE METHODS
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2ND OPPORTUNITY