POLYTECHNIC OF NAMIBIA SCHOOL OF HEALTH AND APPLIED SCIENCES DEPARTMENT of MATHEMATICS AND STATISTICS QUALIFICATION: Bachelor of Technology Accounting and Finance; Diploma in Accounting and Finance QUALIFICATION CODE: 23BACF; 06DPAF COURSE NAME: COURSE CODE: QUANTITATIVE METHODS QTM511S DATE: DURATION: MARKS: JUNE 2013 3 HOURS 100 St 1sl OPPORTUNITY EXAMINATION EXAMINER: MRS S. MWEWA, F NDINODIVA, Y SHAANIKA, DR IKO AJIBOLA, D NTIRAMPEBA MODERATOR: MR. J. SWARTZ INSTRUCTIONS: a. Answer all the questions in the booklet provided b. Show clearly all the steps used in the calculations c. All written work MUST be done in blue or black ink and sketches must be done in pencils. PERMISSABLE MATERIAL 1. Calculator APPENDIX: 1) Formulae Sheet 2) Graph paper ce answer sheet and appendices*
MULTIPLE-CHOICE ANSWER SHEET -QTM511S JUNE EXAM 2013 (MEMORANDUM) STUDENT NUMBER Please iridicate your answers to Section 1 and Section 2 on this answer sheet. Section 1(2 marks each) Section 2(3 marks each) 1.1.1 2.1.1 1.1.2 2.1.2 1.2 2.2.1 1.3 2.2.2 1.4 2.3.1 1.5 2.3.2 1.6.1 2.4.1 1.6.2 2.4.2 1.7 2.5 1.8 Page 1 of 1
Section 1(2 marks each=20 marks) Indicate your answers to this section on the multiple question answer sheet provided. 1.1 Given that the letters A, B, C or D are represented as follows: A=FV of a lump sum B=PV of a lump sum C=FV of an annuity D=PV of an annuity Indicate by putting letters A, B, C or D in the provided box to classify the following problems: 1.1.1 An amount of N$4000 is invested at 6% compounded daily. What will the final amount be in 5 years? (2) 1.1.2 Tim pays N$3200/month for 4 years for a car, making no deposit. If the loan costs 6% p.a. compounded monthly, what is the original cost of the car? 1.2 Money has time value because: (2) A. Individuals prefer future consumption to present consumption. B. Money can be stolen tomorrow (2) C. Money today is worth more than money tomorrow in terms of purchasing power. D. There is a possibility of not earning return on money invested today. 1.3 Given an investment of N$10,000 for a period of one year, it is better to invest in a scheme that pays: A. 12% interest compounded annually B. 12% interest compounded quarterly (2) C. 12% interest compounded monthly D. 12% interest compounded daily
1.4 If the effective rate of interest compounded quarterly is 16%, then the nominal rate of interest is (2) A. 14.6% B. 15% C. 14.8% D. 15.12% 1.5 How many years will it take for N$ 5000 invested today at 12% p.a. rate of interest to grow to N$160,000? (2) A. 23.65 years B. 23.44 years C. 20 years D. 29.31 years 1.6 The age distribution of students enrolled at a community college for artisans given below: Ages Frequency 18 21 19 25 20 40 21 44 1.6.1 The median age of these students is calculated as (2) A. 40 B. 25 C. 19 D. 20 1.6.2 What is the modal age for these students? (2) A. 40 B. 45 C. 20 D. 21 1.7 The time series component that reflects variability during a single year is called (2) A. Trend B. Seasonal C. Cyclical D. Irregular 1.8 If the estimate of the trend component is 158.2%, the estimate of the seasonal component is 94%, the estimate of the cyclical component is 105%, and the estimate of the irregular component is 98%, then the multiplicative model will produce a forecast of (2) A. 1.53 B. 1.53% C. 153.02% D. 153,020,532
Section 2 (3 marks each=27marks) Indicate your answers to this section on the multiple question answer sheet provided. 2.1 The ages of a group of patients being treated at Chumi hospital for cancer are summarized in the frequency histogram below. Frequency 600-500 - 400-300 - 200-100 0 10 20 30 40 50 60 70 80 90 Age of patient 2.1.1 Which of the following best describes the shape of the distribution? (3) A. Positively skewed B. Symmetric C. Negatfvely skewed D. Bimodal 2.1.2 Calculate the approximate modal age at which cancer occurs from the above histogram (3) A. 77 B. 70 C. 80 D. 75
2.2 For the following time series, you are given the moving average forecast. Time Period Time Series Value Moving Average Forecast 1 23 2 17 19 3 17 20 4 26 18 5 11 20 6 23 P 7 17 2.2.1 Which forecasting method is being used here? (3) A. linear regression B. 3-point centered moving average C. 3-point moving average D. Exponential smoothing 2.2.2 From the method selected in 2.2.1, determine the value of P (3) A. 20 B. 17 C. 19 D. 23 2.3 The hourly wages of a sample of 130 accounting system analysts were statistically analyzed and the results are given below: Mean = 60 Range = 20 Mode = 75 Variance = 324 Median = 74 2.3.1 The coefficient of variation of this sample equals (3) A. 0.30% B. 30% C. 5.4% D. 54% 2.3.2 From the above information the shape of the distribution can be determined to be (3) A. Symmetric B. Positively skewed C. Negatively skewed D. Leptokurtic»
2.4 Use the following table to answer questions Data for selected vegetables purchased at wholesale prices for 1995 and 2010 are shown below. (Take 1995 to be the base year) 1995 2010 Price(N$) Quantity Price(N$) Quantity Cabbage(lgram) 0.06 2000 0.05 1500 Carrots (bunch) 0.10 200 0.12 200 Tomatoes (1gram) 0.20 400 0.18 500 Broccoli(bunch) 0.30 100 0.50 200 2.4.1 What is the unweighted aggregate price index? (3) A. 98.4 B. 107.0 C. 117.5 D. 128.8 2.4.2 What is the value of the Laspeyres price index from the table? A. 98.4 B. 107.0 C. 108.0 D. 117.5 (3) 2.5 If A and B are independent events, with P(A orb} is ec!ual to is to (3) A. A 25 B. 10 C. 11 25 D. 1
Section 3(53 marks) Show your calculations to this section clearly and neatly in the answer booklet provided. 3.1 When considering the purchase of a house, Mr. Oshikundu has to take the following into account: The house is on the market for N$970 000 He has N$180 000 available as a deposit The Bank's condition for granting a mortgage bond (loan) for the balance is that his monthly repayments may not exceed ^/3 of his monthly salary. His salary is N$25 500 per month The bank is offering mortgage bonds at 16.25% p.a compounded monthly, repayable in equal monthly instalments over 20 years. 3.1.1 Show that Mr. Oshikundu does not meet the 'third requirement' above. Justify your answer. (8) 3.1.2 As Mr. Oshikundu is determined to purchase the house, he decides on a twopronged strategy: to put in an offer to purchase which is N$50 000 less than the asking price; pay a deposit of N$180000 and to ask the bank to let him repay the bond over a period of 30 years. Calculate the monthly payments Mr. Oshikundu will need to pay to amortize the loan if the bank agrees to Mr. Oshikundu's two-pronged strategy. i(6)
3.2 The following is the frequency distribution for the speeds of a sample of 35 vehicles travelling on Mandume Ndemufwayo Avenue which has a speed limit of 60km/h. Speed (km/h) 50-54 55-59 60-64 65-69 70-74 75-79 Number of vehicles 2 4 5 10 9 5 3.2.1 Compute the mean speed on this avenue and give interpretation of your result. (6) 3.2.2 At which actual speed do 50% of the motorists on this road drive above? (6) 3.2.3 Compute the standard deviation of this data and give interpretation of this result with respect to the information at hand. (9)
3.3 A massage parlour located on the outskirts of Windhoek has the following history of customers over the last four years (data are in hundreds of customers): QUARTER 1 2 3 4 2009 3.5 2.9 2.0 3.2 2010 4.1 3.4 2.9 3.6 YEAR 2011 5.2 4.5 3.1 4.5 2012 6.1 5.0 4.4 6.0 3.3.1 On the graph paper provided plot the above figures joining the points with straight lines. Use 2cm on the vertical axis (y-axis) to represent 1 unit 3.3.2 Calculate a 3-period centred moving average for this data (rounded to one decimal place). (5) 3.3.3 Plot these values on the same graph required in 3.3.1 (3) 3.3.4 Indicate your observations on the original trend line and hence indicate the purpose of plotting moving averages. (4) (6) END OF EXAMINATION GOOD LUCK!
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SUMMARY OF FORMULAE QTM511S Simple Interest: JUNE 2013 EXAM = Prt Compound Interest: Effective Interest Rate Teff ~ l-rt Effective Interest Rate 772 Discount = A(l-dt) = Adt Nominal Interest Rate Ordinary Annuity Certain Ordinary Annuity Certain Sn=R r m r m R = ^- 7? =i " nulog S- log P mlog 1 + V m} n = log 2 log 1 + m for N>2
Measures of Central Tendency Mean N I/ Median Mode J\ Measures of dispersion Variance = n-l \2 \ or Variance = coefficient of variation = xloo n-l (x Index Numbers Laspeyres price index = ~?) ' (-x 100% Paasche price index = ^; ' ^x 100% Laspeyres quantity index = 'o Paasche quantity index = ~; ' ( x 100% Time Series Probability