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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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Sketch Graph(s) to show the following critical points on a cost or revenue function:
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Suppose that Mr. Kuu, a retired chartered accountant, is facing a decision about where to invest the remaining small fortune after deducting the anticipated expenses for the next year from his consultancy earnings. An investment analyst has suggested two types of investments, and to help make the decision, he obtained some rates of return from each type. He would like to know what he can expect by way of the return on his investment, as well as other types of information, such as whether the rates are spread out over a wide range (making the investment risky) or are grouped tightly together (indicating a relatively low risk). The returns for the two types of investments are listed below:
If he decides to group the returns according to classes 19-10, 9-0, 1-10, 11-20, 21-30, 31-40 :
Required:
a) Draw histograms for each set of returns. (5 marks)
b) Compute the following measures of central tendency for the set of returns:
i) Mean (3 marks)
ii) Median (3 marks)
iii) Mode (3 marks)
c) Compute the following measures of spread for the set of returns:
i) Standard deviation (3 marks)
ii) Coefficient of variation (2 marks)
d) Based on (a), (b), and (c), which investment should Mr. Kuu choose and why? (1 mark)
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Maame TorTor borrows GH¢3,000.00 and agrees to pay interest quarterly at an annual rate of 8%. At the same time, she sets up a sinking fund in order to repay the loan at the end of 5 years. The sinking fund earns interest at the rate of 6% compounded semi-annually.
Required:
Determine the size of each semi-annual sinking fund deposit. (5 marks)
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Maame TorTor has just purchased a GH¢70,000.00 house and made a down payment of GH¢15,000.00.
Required:
i) Determine how much money is needed to amortize (i.e., pay monthly) the balance at a 9% interest rate compounded annually for 25 years. (5 marks)
ii) Determine the total interest for the 25 years. (2 marks)
iii) Determine after 20 years the equity she has in the house. (3 marks)
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One of the most important applications of annuities is the repayment of interest-bearing debts. These debts can be paid by making periodic deposits into a sinking fund, which is used at a future date to pay the principal of the debt, or by making periodic payments that cover the outstanding interest and the principal. This second method is called amortization.
Required:
i) Explain the term annuities as used in the statement above. (2 marks)
ii) What is a sinking fund? (2 marks)
iii) When is a loan with a fixed rate of interest said to be amortized? (1 mark)
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The Branch Manager of a building material production plant feels that the demand for iron rod shipments may be related to the number of construction permits issued in the country during the previous quarter. The Manager has collected the data shown in the table below:
| Construction Permits | Iron Rods |
|---|---|
| 15 | 6 |
| 9 | 4 |
| 40 | 16 |
| 20 | 6 |
| 25 | 13 |
| 25 | 9 |
| 15 | 10 |
| 35 | 16 |
Required:
i) Use the normal equations of the least square regression method to derive a regression forecasting equation for the data. (9 marks)
ii) Interpret your regression coefficient in (i) above. (1 mark)
iii) Using the regression line in (a) above, determine a point estimate for Iron Rods when the number of construction permits is 30. (2 marks)
iv) Is your estimate in (iii) above reliable? Give reason(s) for your answer. (2 marks)
v) Calculate the coefficient of determination and interpret it. (6 marks)
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JinJin Company Limited makes two types of leather belts: Type Superior and Type Standard. Type Superior is of high quality, and Type Standard is of lower quality. The respective profits are GHp 40 and GHp 30 per belt. The production of each Type Superior requires twice as much time as a Type Standard belt, and if all belts were of Type Standard, the company could make 1,000 belts per day. The supply of leather is sufficient for only 800 belts per day (both types combined). Belt Type Superior requires a fancy buckle, and only 400 of these are available per day. There are only 700 buckles a day available for Type Standard.
Required:
a) Formulate this problem as a Linear Programming Model. (4 marks)
b) Set up the initial Simplex Tableau. (4 marks)
c) Solve your Tableau in (b) above. (8 marks)
d) Interpret your final Simplex Tableau. (4 marks)
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If selected by the panel, the probability that an ICAG-qualified member will remain with the Private University is 0.6, and the probability that a Chartered Accountant earns more than GHC 5,000 per month in the university is 0.5. If the probability that Mr. Agbagba will remain with the university or earn more than GHC 5,000 per month is 0.7:
Required:
Calculate the probability that he will earn more than GHC 5,000 per month given that he is a Chartered Accountant who will stay with the university.
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Mr. Agbagba, an ICAG qualified member, and his wife, an ICAEW qualified member, attended an interview for two vacancies for the post of College Finance Officer at a Private University. The probability of the interview panel selecting the man is 1/7, and that of the wife is 1/5.
Required:
Assuming the event of selecting a man and selecting a woman are independent, determine the probability that:
i) Both of them will be selected. (3 marks)
ii) Only one of them will be selected. (3 marks)
iii) None of them will be selected. (3 marks)
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Distinguish between the following terms as used in probability:
i) Independent Events and Dependent Events. (2 marks)
ii) Mutually exclusive Events and Exhaustive Events. (2 marks)
iii) Marginal Probability and Joint Probability. (2 marks)
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