I'IHITIIBIFI UNIVERSITY

OF SCIEI'ICE FIND TECHHOLOGYFacultyofHealthand Applied Sciences

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 ;O7BACP;LEVEL: 5

O6BDAF; 07ADTA

COURSE: QUANTITATIVE METHODS COURSE CODE: QTMSllS

SESSION: June 2017 PAPER: THEORY

DURATION: 3Hours MARKS: 100

FIRST OPPORTUNITY EXAMINATION QUESTION PAPER

EXAMINER(S) Mr. F Ndinodiva; Ms. S Mwewa; Ms. Y Shaanika; Dr. I Ajibola; Mr. D

Ntirampeba

MODERATOR: Mr. J Swartz

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 4 PAGES INCLUDING THIS FRONT PAGE (Excluding the formula

sheet)

Question 1147 marks)

1.1

1.2

1.3

1.4

1.5

1.6

1.7

A principal of 2100.00 was invested at a simple interest rate of 8% p.a. For how long will the

principal earn a simple interest of 1300.00? Leave your answer in exact time based on a leap

year. [5]

Selma borrowed N$1000 due at the end of7 months. Determine how much Selma will pay at a

simple interest rate of 9% at the end of 4 months. [7]

Pombili Want N520 000 to finance her trip to Germany. What size loan should Pombili ask for

to get N$20 000 if the bank agrees to a 9 ‘/z % discount rate for 18 months? And calculate the

discount on the loan [6]

Mr. Dix paid a discount note at an annual effective interest rate of 7.5% for 45 days. What is the

corresponding simple discount rate? [6]

Mr. Etu had a note of N515000 dated 14 February 2017, with an interest rate of 7% p.a.

compounded three times a year. The maturity date was 90 days after date. Calculate how much

Mr. Etu will pay on 29 February 2017 if money is worth 3%p.a. compounded yearly. [7]

A yearly sum of N$3600 is deposited periodically for six years into a fund that earn interest at

5% p.a compounded monthly. Find how much the amount of the deposits will be at the end of

ten years, if no money was withdrawn or deposited in the account after the last periodical

deposit was made. [9]

Mr. Katemba deposited N52650 on 01 January 2007 in an account paying interest at 7%

compounded quarterly. Find how much will be in the account on 20July 2017? How much is the

compound interest during the time? [6]

Question 2 |28 marks|

2.1

2.2

2.3

A sample of 30 delivery times taken by a courier service to deliver parcels from Ongha to

Eenhana is shown in the frequency table Below

Time(minutes) 5 - <10 10 - <15 15 - <20 20 — <25 25 - <30

Frequency 3 5 9 7 6

Use the data set to calculate and interpret the coefficient of variation. [12]

The following information shows the sales of the Toyota Company during the year 2008 -2016.

Year: 2008 2009 2010 2011 2012 2013 2014 2015 2016

Sales: 75.3 74.2 78.5 79.7 80.2 85.2 84.3 76.4 89.6

2.2.1. Use the data to determine the least squares trend line equation, using the

zero sum coding method. [6]

2.2.2 Hence estimate the trend value for Toyota company for 2003 [2]

The table below shows the number of CD5 and MP3s purchased per annum and their prices.

It shows that the number of CDs purchased decreases over time, whilst the number of MP3s

rises as technology improves and newer products begin to replace older ones.

Year Number purchased Amount spend

price (£) per annum on

CD5 MP3$ CDs MP3s CDs MP3s

2004 12 8 9 3 108 24

2005 13 6 6 9 78 54

2006 14 5 4 14 56 70

In order to calculate the combined 'music’ series, it is necessary to create a weighted average

of the two component series using the base year weights (2004). Use the data to calculate the

Laspeyres quantity and paasche Quantity indexes for year (2005). [8]

Question 3 |25 marksl

3.1

3.2

3.3

3.4

Consider the following system:

2x+y—z=3

x+y+z=1

x—2y—3z=4

3.1.1 Write the system as a matrix equation. [3]

3.1.2 Reduce the system into triangular form using Gaussian elimination or Matrices. [5]

Tickets numbered from 1 to 20 are mixed and then a ticket is drawn at random. What is the

probability that the ticket drawn has a number which is a multiple of3 or a multiple of 5? [4]

A bag contains 21 toys numbered 1 to 21. A toy is drawn and then another toy is drawn without

replacement. Find the probability that both toys will show even numbers. [4]

Hangula Commuter Airways recently supplied the following information to the Government on

their commuter from Windhoek to Oluhapa.

Arrival Frequency

Early 100

On Time 800

Late 75

CanceHed 25

Let A be the event that a flight arrives early and B be the event that a flight arrives late.

3.4.1 Are events A and B mutually exclusive? Explain? [2]

3.4.2 Are events A and B collectively exhaustive? Explain? [3]

3.4.3 What is the probability that a flight is either early or late? [4]

END OF THE EXAM

SUMMARY OF FORMULAE QTM51 1S

JUNE/July 201 7 EXAM

Simple Interest: 1 = P”

Compound Interest: A = P(1+i)

7"

Effective Interest Rate refl:

_ rt

Effective Interest Rate Fef/ =[1+7;—) -1

Discount P = A(1— dz‘) D = Adt

d _

r

Simple discount Rate1 + rt

Nominal Interest Rate

Ordinary Annuity Certain

(Hi) —1

s,,=R ———’"’7'

I72

r=m[(1+reff)i 4]Ordinary Annuity Certain

1—(1+L]A” 2R _m_

1"

m

. 1 S—1 P 10 2Pernod t=——————°g0g ——g—-—

r r

mlog[1+—] log[l+—jm m

i5 i4N—l 10 —”+1 10(1——’)

t: for N22": g(R ):_

gR

I” log(1+i) log(1+i)

Measures of Central Tendency

Mean 32:? EZEJ:Median Md =1Md +11 2——

fi—foMode +[(f1_fo)+(f1_f2):|Measures of dispersion

2_

_ 2

_—__Zficn(x)or Variance =

n—1 n—1

Standard deviation=\/ variance

Variance =

Index Numbers

P P. .

Laspeyres price index = Z2—(fi&)—x 100% Paasche price index =M x100%

ZUibe) Z(B,><Q,-)

Laspeyres quantity index = —%(Lf-X%%x 100% Paasche quantity index =—% x100%

bx

b ix

b

Time Series

“_ b b_nZw-Zx2y _Zy-bey

— a + x —-

Wa —

——n-

Probability

P(AuB)=P(A)+P(B)—P(AnB) P(AmB)=P(A)P(B)

P(AnB)P (A)

P(B|A)=