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A loan of GH¢3,000 at an effective annual interest rate of i = 12% is amortized by means of 12 annual payments, beginning a year after the loan is taken.
Hint: The schedule should have the following columns: Payment, Interest Due, Principal Repaid, and Outstanding Balance.
Required:
Construct an amortization schedule.
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b) Use the sample data below to answer the following questions:
Required:
i) Calculate the sample mean, variance, and standard deviation for X. (5 marks)
ii) Calculate the sample mean, variance, and standard deviation for . (5 marks)
iii) Calculate the sample covariance between X and Y. (3 marks)
iv) Calculate the sample correlation between X and . (3 marks)
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a) If the total cost (in Ghana cedis) of producing xx items is given by the function C (x) = 2600 + 2x + 
Required:
i) Calculate the total cost, average cost, and marginal cost of producing 5000 items. (6 marks)
ii) Determine the production level at which the average cost will be the lowest. (4 marks)
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a) Receipts at a particular depot have amounts which follow the Normal distribution with a mean of GH¢103.60 and a standard deviation of GH¢8.75.
Required:
i) Determine the percentage of receipts over GH¢120.05.
ii) Determine the percentage of receipts below GH¢92.75.
iii) Determine the percentage of receipts between GH¢83.65 and GH¢117.60.
iv) Determine the receipts amount such that approximately 25 percent of receipts are greater.
v) Above what amount will 90 percent of receipts lie?
b) If 10.56 percent of receipts have an amount above GH¢110.05 and 4.01 percent of receipts have an amount above GH¢120.05.
Required:
Calculate the mean and standard deviation of the receipts assuming that they are normally distributed.
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a) If from a normal pack of 52 cards, consisting of four suites each of 13 cards, one card is randomly selected:
Required:
Calculate the probabilities of selecting the following:
i) An ace
ii) A club
iii) An ace or a club
iv) The ace of clubs
v) A picture card (i.e. a jack, queen or king)
vi) A red card
vii) A red king
viii) A red picture card
b) Given that a card selected is red, calculate the probability that it is a picture card.
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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)
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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 four 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 the 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.
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Kyerewaa Ventures is a manufacturing company in the business of producing beverage cans for clients in the brewery industry. The weekly total cost to produce x cans is given by:
The demand function for the cans is given by:
The company has set a 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 2,501st can is produced and sold. (3 marks)
iii) Determine the cost, revenue, and profit when the 7,501st can is produced and sold. (3 marks)
iv) Advise the company whether to produce the 2,501st can or the 7,501st can. (2 marks)
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The distribution of the total loan amounts defaulted by customers of a bank annually is approximated by a normal distribution. The 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¢2 million. (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)
(Total: 20 marks)
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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:
| Access Time (Minutes) | Number of Patients |
|---|---|
| 15 – 19 | 2 |
| 20 – 24 | 5 |
| 25 – 29 | 8 |
| 30 – 34 | 10 |
| 35 – 39 | 13 |
| 40 – 44 | 17 |
| 45 – 49 | 20 |
| 50 – 54 | 16 |
| 55 – 59 | 12 |
| 60 – 64 | 15 |
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)
(Total: 20 marks)
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A small business is interested in the relationship between the number of hits on its website (measured by the number of visitors that have used the main menu) and the level of website promotion (in GH¢ 00s). The table below gives the figures for the last six months:
| Month | Web Site Hits | Web Site Promotion (GH¢ 00s) |
|---|---|---|
| 1 | 25 | 1.0 |
| 2 | 24 | 1.2 |
| 3 | 56 | 1.6 |
| 4 | 54 | 1.4 |
| 5 | 55 | 1.2 |
| 6 | 58 | 1.8 |
Required:
a) Graph the number of website hits against website 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 website hits 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)
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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 simplex 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)
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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.
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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.
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