Alpha Transport Company buys a vehicle for GH¢265,000. The value of the vehicle depreciates on a reducing balance basis at 17% per annum. The company plans to replace this vehicle in 5 years’ time and they expect the price of a new vehicle to increase annually by 12%.
Required:
i) Calculate the book value of the vehicle in five years’ time.                                                                                             (3 marks)

ii) Determine the amount of money needed in the sinking fund for the company to be able to afford a new vehicle in five years’ time.                                                                                                                                                                                    (3 marks)

iii) Calculate the required monthly deposits if the sinking fund earns an interest rate of 11% per annum compounded monthly. (3 marks)

Every Monday, Kwei puts GH¢30 into a savings account at the Ring Bank, which accrues interest of 6.92% per annum compounded weekly.
Required:
i) Draw a cash flow timeline showing the payments, the interest rate and the present values for the first 4 payments.    (3 marks)

ii) Determine how long it will take Kwei’s account to reach a balance of GH¢4,397.53. Convert your answer into number of years and days to the nearest integer.                                                                                                                                  (6 marks)

iii) Determine how much interest Kwei will receive from the bank during the period of his investment.                         (2 marks)

a) Distinguish between marginal cost and average cost in production.                                                                               (2 marks)

The company has set production limit to 10,000 Cans and it sells all the Cans that are produced.
Required:
i) Derive an expression for marginal cost, marginal revenue and marginal profit.                                                             (4 marks)

ii) Determine the cost, revenue and profit when the 2501st Can is produced and sold.                                                     (3 marks)

iii) Determine the cost, revenue and profit when the 7501st Can is produced and sold.                                                    (3 marks)

iv) Advise the company whether to produce the 2501st Can or the 7501st Can.                                                                (2 marks)

c) If, after expanding its facilities, the company is capable of producing 60,000 Cans in a day and the total daily cost is given by

Required:
How many Cans per day should they produce in order to minimize production costs?                                                     (6 marks)

The distribution of the total loan amounts defaulted by customers of a bank annually is approximated by a normal distribution. An average default amount is GH¢1.50 million and the standard deviation is GH¢0.50 million.
Required:
a) Determine the probability that the total loan amount defaulted exceeds GH¢1.50 million.                                           (3 marks)

b) Determine the probability that the total loan amount defaulted is between GH¢0.86 million and GH¢0.90 million.   (4 marks)

c) Determine the probability that the total amount defaulted is at most GH¢2million.                                                      (4 marks)

d) Determine the amount to be allowed per annum for loan defaults if 1% of actual defaults exceed this amount.          (3 marks)

e) Determine the lower quartile of the distribution of total loan amounts defaulted.                                                          (3 marks)

f) Determine the upper quartile of the distribution of total loan amounts defaulted.                                                          (3 marks)

Data on access time, in minutes, to a medical consultant who charges by the hour was recorded by his accountant’s assistant over a period of one week. Using a class width of 4 minutes, the following frequency distribution table was obtained:

Required:
a) Using a graph sheet draw a less than or a greater than (more than) cumulative frequency curve (ogive) of the data.   (6 marks)

b) From the ogive in (a) above estimate the median access time.                                                                                       (2 marks)

c) Calculate the mean and the mode of the access times.                                                                                                    (6 marks)

d) Calculate the standard deviation of the distribution.                                                                                                       (4 marks)

e) Using, the values in (b) and (c) above, comment on the skewness of the distribution.                                                  (2 marks)

A small business is interested in the relationship between the number of hits on its web site ( measured by number of visitors that have used the main menu) and the level of web site promotion (in GH¢ 00s). The table below gives the figures for the last six months;

Required:
a) Graph the number of web site hits against web site promotion.                                                                                     (2 marks)

b) Comment on any possible relationship in (a) above.                                                                                                      (2 marks)

c) Calculate the correlation coefficient and give an interpretation to its value.                                                                  (5 marks)

d) Determine the regression line.                                                                                                                                         (5 marks)

e) Using the regression line found in part (d) above, predict the number of web site hit if the level of monthly promotion were increased to GH¢200.                                                                                                                                                          (2 marks)

f) Comment on the reliability of your prediction in (e) above.                                                                                             (1 mark)

g) Comment on the simple forecasting model you have developed above.                                                                        (3 marks)

An advertising agency wishes to reach two types of audiences: Customers with annual income greater than GH¢ 15,000 (target audience A) and customers with annual income less than GH¢15,000 ( target audience B). The total advertising budget is GH¢ 200,000. One programme on TV advertising costs GH¢50,000; one programme on radio advertising costs GH¢20,000. For contract reasons, at least three programmes ought to be on TV, and the number of radio programmes must be limited to five. Surveys indicate that a single TV programme reaches 450,000 customers in target audience A and 50,000 in target audience B. One radio programme reaches 20,000 in target audience A and 80,000 in target audience B.
Required:
i) Formulate the linear programming problem.                                                                                                                  (4 marks)

ii) Construct the initial simplest tableau.                                                                                                                            (4 marks)

iii) Perform the first iteration.                                                                                                                                             (4 marks)

iv) Determine the media mix to maximize the total reach.                                                                                                 (4 marks)

v) Determine the shadow prices of the binding constraint.                                                                                                 (4 marks)

The Asogli Company Ltd has been offered the following alternative terms for a one year loan to be repayable plus the interest in full at the end of the year:
i) 2.5% per month compounded monthly
ii) 10% per six months compounded six-monthly.
Required:
Calculate, for each alternative the annual percentage rate of interest. Recommend one of the alternatives and explain why.  (10 marks)

a) Accra Junction Mall sells apples either for GH¢10 per kg or in bulk GH¢180 per 20 kg. What is the percentage saving per kg from buying in bulk?                                                                                                                                                           (2 marks)

b) Solve the following expression;                                                                                                                                      (3 marks)

i)

ii)

c) A compound house at Ashaiman has a simple meter. There are 5 units’ chamber and hall within the compound. The total electricity bill submitted by ECG for the month of September 2017 was GH¢2,700. The outstanding bill on the month of August 2017 was GH¢1,000.
Required:
Calculate the bill for each tenant for the month of September 2017 if the tenants had agreed to share the bill in the ratio 2:3:4:5:6.                                                                                                                                                                              (5 marks)

The following data gives how much 10 students of ICAG spend on TroTro to the Institute and food weekly .

Required:
a) Using a graph paper, construct a scatter diagram of the data.                                                                                         (4 marks)

b) Determine, the correlation coeficient.                                                                                                                             (4 marks)

c) Calculate, the coefficient of determination of the data and interpret its value.                                                               (4 marks)

d) Determine the regression line of y on x , and interpret the coefficient.                                                                          (8 marks)