THE INSTITUTE OF CHARTERED ACCOUNTANTS (GHANA) QUANTITATIVE TOOLS IN BUSINESS QUESTION PAPER NOVEMBER 2014

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Phebe Underwood
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1 QUESTION 1 THE INSTITUTE OF CHARTERED ACCOUNTANTS (GHANA) Given the cost function c=5x and the demand function p=29-4x, x being the quantity of goods. Find the optimum price. (5 marks) Find the quantity before and after tax of GH 1 per unit is imposed. (5 marks) Find the tax rate that will maximize tax revenue (5 marks) (iv) Determine the tax revenue if an additional tax of 20% is imposed. (5 marks) QUESTION 2 The error identified in a number of transactions have been recorded in the following table. Those that have led to a loss are recorded as a negative and those that have a gain as a positive. Error - GH but less than - GH 50 - GH 50 but less than - GH 10 - GH 10 but less than 0 0 but less than GH 10 GH 10 but less than GH 50 GH 50 but less than GH Number of transactions (a) Determine: the mean, median, mode (6 marks) the first quartile, third quartile, interquartile range (6 marks) the variance (2 marks) (b) Calculate the absolute mean deviation and comment on its value. (6 marks)

2 Page 1 of 6 QUESTION 3 A used car dealer randomly selected hundred () 3-year-old Toyota Camrys that were sold at an auction during the past month. Each car was in top condition and equipped with all the features that come standard with this car. The dealer recorded the price (GH 000) and the number of miles (thousands) on the odometer. Some of these data are listed here. Car Price (GH 1,000) Odometer Let y be the selling price of cars and x the odometer reading of cars. From the data set, the dealer obtained the following statics: xi = 3,601.1, yi = 1,484.1 xiyi = 53, xi² = 133, (a) Calculate the sample slope coefficient (3 marks) Calculate the y-intercept (3 marks) Interpret your results in and above (3 marks)

3 (iv)write the regression equation. (3 marks) Page 2 of 6 (b) The dealer analyzed the data using Microsoft Excel Package and obtained the following results: Interpret the coefficient of determination (4 marks) Comment of the validity of the regression mode in (a) above (4 marks) QUESTION 4 (a) Explain the term Annuity in finance (b) Give five (5) examples of annuity (1 mark) (5 marks) (c) J. Kaburuku is repaying a debt with payments of GH 2500 a month. If he misses his payments for July, August, September and October, and interest is at 14.4% compounded monthly; Find a single payment that can be made in November to put him back on schedule. (4 marks)

4 (d) J. Kaburuku deposited GH 3000 at the end of each year into a retirement savings plan with Donegood Insurance Company Ltd for the last 10 years. His deposits ended 8% Page 3 of 6 (e) Compound interest per annum for the first 3 years; 10¼ compound interest per annum for the 4 years and 9% compound interest per annum for the last 3 years. Find the accumulated value of the retirement plan. (4 marks) Find the total interest earned for the 10 years. (2 marks) (f) J. Kaburuku also opens a saving account with a Rural Bank with deposit of GH 2000 on February 1, 2003 and makes monthly deposits of GH 200 for 5 years, starting March 1, Starting March 1, 2008, he makes monthly withdrawals of GH 400 for 3 years. If the account earned 6% compound interest per month; Find the balance in his account just after the last withdrawal on February, (4 marks) QUESTION 5 (a) Define the following terms under probability Sample space Sample point An event (b) The following table illustrates the distribution of workers of Private Security Companies: A, B, C and D at an outpost which runs a two shift system Day Shift and Night Shift. DAY SHIFT NIGHT SHIFT MALE FEMALE MALE FEMALE TOTAL A

5 B C D TOTAL Page 4 of 6 (a) If a worker is selected at random from the outpost, calculate the probability that the worker selected is A female A male from the Company C A night-shift worker from the Company B (7 marks) (b) If a night-shift worker is selected at random from the outpost, find the probability that the worker is A male From the Company D A female from the Company C (7 marks) QUESTION 6 (a) Explain the following terms in Stock Control Economic order quantity Price discount Marginal cost (6 marks) (b) Kukuoma Company Ltd uses a special bracket in the manufacture of its products which it orders from outside suppliers. The demand for the brackets is 20,000 per annum. Order cost is 2000 per order. Carrying cost is 20% of item price where an item price is GH per bracket.

6 The company is offered the following discounts on the basic item price. For order quantities 4, less 4% 8, less 8% 16,000 and above less 10% Page 5 of 6 Find the most economical order quantity. (14 marks) QUESTION 7 The management of Odeneho Transport Company (OTC) plans to expand its fleet of buses for the next quarter by purchasing Mini and Long Buses. The average cost of a Mini bus is GH 10,000 and the average cost of a Long bus is GH A total of 800 buses are to be purchased with a budget of GH 12million Formulate the system of linear equations of the above information (4 marks) Using matrix inversion method, how many buses of each type will be acquired? (10 marks) The predicted demand calls for a total purchase of 0 buses a budget of GH 14million. How many buses of each type will be acquired? (6 marks) Page 6 of 6

1. Find the slope and y-intercept for

1. Find the slope and y-intercept for MA 0 REVIEW PROBLEMS FOR THE FINAL EXAM This review is to accompany the course text which is Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, th Edition by Barnett, Ziegler,