nAmIB I A U n IVERS lTV OF SCIEnCE AnD TECHnOLOGY

Faculty of Health and 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 ;07BACP; LEVEL: 5

06BDAF;07ADTA

COURSE: QUANTITATIVE METHODS COURSE CODE: QTM511S

SESSION: June 2016 PAPER: THEORY

DURATION: 3 Hours MARKS: 100

FIRST OPPORTUNITY EXAMINATION QUESTION PAPER

EXAMINER(S) Mr. F Ndinodiva; Ms. S Mwewa; Ms. Y Shaanika; Ms. L Endjala; Dr. I ajibola;

Mr. 0 Ntirampeba

MODERATOR: Mr. A Roux

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 (Excluding the formula

sheet)

1

Question 1(34 marks)

1.1 When will the simple interest on N$15000 at the rate of 9% p.a be the same as simple interest

on N$8000 at 12% p.a for 4 and half years? [5]

1.2 Mr War owes N$4500 due in 9 months and N$9000 due in 18 months. The lender agrees to

allow Mr War to pay off these debts with a single payment. What single payment

a) Now

b) In 1 year

will liquidate these obligations if money is worth 8%? [10]

1.3 A treasury bill of $10,000 for 13 weeks has a discount value in buying of N$23.90. Find the

actual cost to buy of the Treasury bill and the effective rate of Treasury bill. [4]

1.4 Gwaze invested $5000 in a savings account that paid him quarterly interest. After 6 years he

received $6539.96. At what annual interest rate did Gwaze earn interest? [5]

1.5 Mr Etu deposited N$900 at the end of each month of the calendar year 2015 in an investment

account at 9% annual interest rate. Determine how much Mr Etu will be able to withdraw on

Dec 31, 2015. Compounding is done on monthly basis. [5]

1.6 A principal amount of N$ 3000 is invested for 6 years at 10% compounded half yearly. Find the

compound amount of the principal and the interest paid over that period of time. [5]

Question 2 [21 marks]

2.1 Complete the frequency distribution of an exam given below. [4]

Class Frequency Cumulative Frequency

50 ｾｘ＼＠ 60 2

60 ｾｘ＼＠ 70 5

70 ｾｘ＼＠ 80 21

80 ｾｘ＼＠ 90 17

90 ｾｘ＼＠ 100 12 50

2

2.2 What is a good measure of dispersion between standard deviation and coefficient of

variation? Justify your answer.

2.3 Consider the following information.

Q1 = Il.Sdays

Q2 = I5.89days

Q3 = I9.93days

2.3.1 Calculate the Semi interquartile range

2.3.2 Interpret your answer on 2.3.1 above.

[4]

[2]

[3]

2.4 Below are prices of toothpaste, shampoo, cough tablets, and antiperspirant for August 2000

and August 2003. Also included are quantities purchased.

August 2000 August2003

Item Price Quantity Price Quantity

Toothpaste 2.49 6 2.69 6

Shampoo 3.29 4 3.59 5

Cough tablets 1.59 2 1.79 3

Antiperspirant 1.79 3 2.29 4

2.4.1 Compute and interpret the quantity relative for antiperspirant (use august 2000 as the

base) [3]

2.4.2 Construct a quantity index to reflect the overall change in quantities purchased for the

period 2000-2003. Use the Paasche approach. Interpret your index. [5]

3

Question 3 (21 Marks)

Suppose the following quarterly sales (in thousands) have been recorded by Etosha national park

head office for the years 1999 to 2003.

Quarter

Year Winter Spring Summer Autumn

1999 117 80.7 129.6 76.1

2000 118.6 82.5 121.4 77

2001 114 84.3 119.9 75

2002 120.7 79.6 130.7 69.6

2003 125.2 80.2 127.6 72

3.1 Compute the 4-period centered moving average for the quarterly sales. [8]

3.2 Use the method of least squares from regression analysis to determine the trend line of best

fit. Use the zero-sum method for coding. [10]

3.3 Using the trend line you produced in 3.2, estimate the trend value of the time series for

summer in 2004.

Question 4 [24 marks]

4.1 Is the following system a homogeneous or a heterogeneous? Why?

4x+ y+z =0

3x-2y+3z = 0

2x- y-z =2

4.2. What is the trivial solution of the homogeneous system?

4.3 Solve the following system of equations

x+ y +z=3

x- y+2z =2

3x- y+Sz = 7

4

[3]

[3]

[2]

[6]

4.4 The following table shows household income by educational level of the head of household

(Statistical Abstract of the United States, 2008).

Household income in US$ 1000

Educational level under25 25-49.9 50- 75-99.9 100 or Tot

74.9 more

Not H.S graduate 4207 3459 1389 539 367 9961

H.S graduate 4917 6850 5027 2637 2668 22099

Some college 2807 5258 4678 3250 4074 20067

Bachelor's Degree 885 2094 2848 2581 5379 13787

Beyond 290 829 1274 1241 4188 7822

Bach.Degree

Tot 13106 18490 15216 10248 16676 73736

4.4.1 What is the probability of a household headed by someone with educational level beyond a

bachelor's degree or by someone earning between $50000 and $74900? [3]

4.4.2 What is the probability of a household headed by someone with a bachelor's degree earning

$100,000 or more? [3]

4.4.3 What is the probability of a household headed by someone who is not a high school graduate?

[2]

4.4.4 If a household with income under $25000 is selected at random, what is the probability that it

is headed by someone with a bachelor's degree? [5]

END OF THE EXAM

5

. \

SUMMARY OF FORMULAE QTM511S

JUNE 2016 EXAM

Simple Interest: I= Prt

Compound Interest: A= P(l + i)n

r Effective Interest Rate ref! = I- rt

Effective Interest Rate r,JJ = (I+ : r -I Discount P=A(l-dt) D=Adt

Ordinary Annuity Certain Ordinary Annuity Certain

m

A R=-n a-, .

1111

t = _I o--=g_S__,.-_1 o__;;g=--P..,....

mlog(l+ ｾＩ＠

iS log(-" +1)

n= R log(l + i)

R = s/1 S,.

/111

log2 n = --;-=----:-

ｬｯｧＨｬＫｾＩ＠

n=

111

log(l- iA,, ) R

log(l + i)

1

m

N-1 t = for N?::. 2

r

..., \, I ,t \

Measures of Central Tendency

Mean - LX x=--

n

- Itx ｘ］ｾＺＭＭＭ

If --F

Median [

n J Mcl=lMcl+h T

Mode

Measures of dispersion

"fx2 (_)2 Variance= L.... - n x or

n-1

I( x-x )' Variance = ---'-' --'-------'--

n-1

Standard deviation=.J variance

Index Numbers

coefficient of variation = ( ｾ＠ )x 100

Laspeyres price index = f i P; x Q, ｾ＠ x 1 00% Paasche price index = f i P; x Q, j x 100% ｾｸｾ＠ ｾｸｑ＠

Laspeyres quantity index = f i P;, x Q, j x 100% ｾｸｑ ｢＠

Time Series

y=a+bx

Probability

n

Paasche quantity index = f i P, x Q, j x 100% P; xQh

P(AuB) = P(A)+P(B)-P(AnB) P(AnB)=P(A)P(B)

(I )_P(AnB) p B A - P(A)

2