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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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Find Related Questions by Tags, levels, etc.
Find Related Questions by Tags, levels, etc.
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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i) Any entity that issues a bond to raise capital would need to pay off the bond when it matures. Paying the debt early via a sinking fund saves a company interest expense and prevents the company from being put in financial difficulties in the future if economic or financial conditions worsen.
Required:
What is a sinking fund? (3 marks)
ii) The owner of a Business Centre purchased a robust photocopier for serving the UG University Students Community. The photocopier is expected to be replaced after 10 years. He therefore decided to set up a sinking fund and pay an equal annual amount to realize GH¢50,000, being the replacement cost.
Required:
Compute the equal annual amount he should invest if the interest rate per annum is 10%. (4 marks)
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Joycarpap Ltd manufactures and sells three models of affordable toys: Car, Joy, and Pap. Each model requires a specific amount of fabrication hours, material worth, and assembly hours as shown in the table below:
There are 210 fabrication hours available, 170 hours of assembly available, and materials worth GH¢200 in stock. Market research conducted by the company revealed that demand for the toys is such that, in whatever combination of the three models produced, all of the output can be sold within a week.
Each Car contributes GH¢15 to profit, each Joy contributes GH¢20 to profit, and each Pap contributes GH¢14 to profit. Using , , as decision variables, and , , as slack variables, and as total profit:
Required:
i) Formulate a linear programming problem. (4 marks)
ii) Set up the initial Simplex Tableau. (4 marks)
iii) Determine the total profit in the first iteration. (5 marks)
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A survey of The Institute of Chartered Accountants (Ghana) students asked the question: “What is your favourite sport?” The results are summarized below:
| Level | Football | Boxing | Hockey | Total |
|---|---|---|---|---|
| 1 | 68 | 41 | 46 | 155 |
| 2 | 84 | 56 | 70 | 210 |
| 3 | 59 | 74 | 47 | 180 |
| Total | 211 | 171 | 163 | 545 |
Required: i) What is the probability of selecting a student whose favourite sport is boxing? (2 marks)
ii) What is the probability of selecting a Level 1 student? (2 marks)
iii) If the student selected is a Level 2 student, what is the probability that the student prefers hockey? (3 marks)
iv) If the student selected is a Level 2 student, what is the probability that the student prefers football or hockey? (3 marks)
v) If the student selected prefers football, what is the probability that the student is a Level 1 student? (3 marks)
vi) If the student selected is a Level 3 student, what is the probability that the student prefers football, boxing, or hockey? (3 marks)
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Find Related Questions by Tags, levels, etc.
The number of enquiries being made to a mail order business during a Monday to Friday working week is given as:
| Week | Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|
| 1 | 34 | 36 | 24 | 25 | 41 |
| 2 | 33 | 34 | 24 | 23 | 43 |
| 3 | 35 | 37 | 25 | 25 | 47 |
Required: i) Plot the data on a graph.
ii) Compute a 5-period moving average for the data.
iii) Compute a ‘weighted’ moving average for the data if the smoothing constant is α=0.5.
iv) Superimpose the graphs of (ii) and (iii) on your graph in (i) above.
v) Comment on the suitability of the two smoothing methods above. (16 marks)
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The objective of smoothing methods is to smooth out the random variations due to irregular components of the time series and provide an overall impression of the pattern of movement in the data over time.
Required:
Explain the following smoothing methods:
i) Moving averages (2 marks)
ii) Exponential smoothing (2 marks)
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CarJoy Manufacturing Company produces electronic components that have life spans normally distributed with mean hours and standard deviation σ hours. Only 1% of the components have a life span less than 3,500 hours and 2.5% have a life span greater than 5,500 hours.
Required:
i) By standardizing the values of to the standard normal values, obtain TWO (2) linear equations in and . (4 marks)
ii) Using an appropriate method of solving simultaneous equations, determine the value of and in (i) above. (4 marks)
iii) Determine the proportion of electronic components with life spans between 4,120.50 hours and 5,052.45 hours. (4 marks)
iv) If the company gives a warranty of 4,000 hours on the components, find the percentage of components the company is expected to replace under the warranty. (4 marks)
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Find Related Questions by Tags, levels, etc.
The Business Manager of Omaya Art Gallery has rented a hall to display the artworks of the artists of the gallery. She is considering organizing an exhibition of a number of rare painting masterpieces. In the past, only 70% of the paintings were sold in the first week. Moreover, if no painting is sold in the first five (5) days, the exhibition could be extended for another two (2) days but only 20% of the paintings would be sold.
The cost of the exhibition is GH¢500 per day. The manager estimated that in case she does not make any sales, she will have to pay GH¢15,000 to cover the costs of renting the exhibition hall for the same period.
Required: a) Draw a decision tree representing the Business Manager’s decision-making process. (8 marks)
b) Calculate the expected monetary cost of each decision node. (6 marks)
c) Determine the Business Manager’s optimal strategy. (6 marks)
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