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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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The secretariat of an association of industries gathered the following data from a random sample of member firms that produce similar products:
Required:
i) Compute the Pearson’s product moment correlation coefficient for the data. (6 marks)
ii) Hence, compute the coefficient of determination. (2 marks)
iii) Comment on your answer in (ii). (2 marks)
iv) Compute Spearman’s rank correlation coefficient for the data and comment on your answer. (8 marks)
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Sketch a scatter graph for two variables (dependent and independent variables) that represents:
i) Perfect positive correlation between the variables. (1 mark)
ii) Perfect negative correlation between the variables. (1 mark)
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The table below shows the range of bi-weekly income of a sample of 50 accountants of a multi-national accounting firm:
| Range of Income (GH₵) | Number of Accountants |
|---|---|
| 80 and Less than 100 | 5 |
| 100 and less than 120 | 4 |
| 120 and less than 150 | 12 |
| 150 and less than 170 | 7 |
| 170 and less than 200 | 8 |
| 200 and less than 250 | 9 |
| 250 and less than 300 | 5 |
Required:
i) Compute all the THREE measures of central tendency of the range of income and comment on the distribution. (8 marks)
ii) Compute the coefficient of variation of the range of income of the accountants. (7 marks)
iii) Interpret your answer in (ii). (1 mark)
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i) Distinguish between measures of central tendency and measures of dispersion (or variation). (2 marks)
ii) State TWO examples of measures of central tendency. (1 mark)
iii) State TWO examples of measures of dispersion (or variation). (1 mark)
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a) Kofy Addo invested GH¢4,000 into his bank account at the beginning of every year for four years. The bank paid interest at 8% compounded annually for the first four years. Thereafter, the interest rate changed to 8.35%, but Kofy Addo did not make any more deposits. At the end of the sixth year, he withdrew GH¢5000.
Required:
i) Calculate the size of the investment at the end of the sixth year, before the withdrawal.
ii) Calculate the size of the investment after the withdrawal in the sixth year.
iii) Calculate the balance in the account after the eighth year.
b) Kofy Addo decided to start saving money for his future. At the end of each month, he deposited GH¢500 into an account at Trust Bank, which earned an interest rate of 9% per annum compounded monthly.
Required:
i) Determine the balance of Kofy Addo’s account after 20 years. (4 marks)
ii) Calculate the amount deposited into the account over the 20-year period. (2 marks)
iii) Calculate how much interest he earned over the 20-year period. (2 marks)
iv) Calculate the effective annual rate of interest. (2 marks)
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a) The quarterly unit sales of electronic items of a retail company for the last three years are as follows:
| Year | Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
|---|---|---|---|---|
| 2013 | 100 | 115 | 70 | 210 |
| 2014 | 120 | 165 | 100 | 220 |
| 2015 | 150 | 195 | 120 | 270 |
Required:
i) Calculate a centered three-moving average of the unit sales. (3 marks)
ii) Calculate the trend using a centered four-quarterly moving average. (4 marks)
iii) Calculate the four seasonal variations using (ii) and the multiplicative model. (7 marks)
iv) Forecast the number of unit sales for the year 2016 using the multiplicative model. (4 marks)
v) Comment on your answer in (iv). (2 marks)
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a) The marginal revenue function of a manufacturing company is given by:
The marginal cost function is given by:
Let x be the number of items either produced or sold.
Required:
i) Calculate the revenue generated when 50 items are sold. (2 marks)
ii) Calculate the number of items that will yield maximum revenue. (4 marks)
iii) Calculate the total revenue if 100 items are produced. (4 marks)
iv) Calculate the total profit for the 100 items. (4 marks)
v) If a tax of 20% is imposed on each item produced, find the cost of 100 items. (6 marks)
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A Ghanaian student studying abroad wants to develop an empirical model for energy consumption (in kilowatts per day) as a function of the daily high temperature (in degrees Celsius) in winter. For nine days the following information was obtained:
| Temperature (°C) | -0.4 | -0.2 | 0.3 | 0.8 | 1.1 | 1.4 | 1.8 | 2.1 | 2.5 |
|---|---|---|---|---|---|---|---|---|---|
| Energy used (kW) | 28 | 30 | 26 | 25 | 26 | 26 | 27 | 26 | 22 |
Required:
a) Identify the response and predictor variables, based on the purpose for developing the regression model. (2 marks)
b) Determine the coefficient of regression and the regression constant. Give your values to 2 decimal places. (5 marks)
c) Interpret your results in b) above. (3 marks)
d) Write the equation of the regression line of energy use on temperature in the form y=a+bxy = a + bx. (2 marks)
e) Estimate the student’s daily energy consumption when the daily high temperature is 2 degrees Celsius. (2 marks)
f) Determine the standard error of estimate. (6 marks)
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The Managing Director of a small manufacturing company is considering buying a piece of machinery which costs GH¢15,000.
Required:
If the machine is to be purchased by taking a five-year loan at 9% per annum, which will be paid off in five equal annual instalments (starting a year after the loan is taken out), calculate the size of each instalment to the nearest whole number. (6 marks)
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You have received a prize amount of GH¢5,000 and you wish to invest it for five years. The two alternatives are to use a bank account where the 14% per annum gross rate is compounded monthly or a savings fund where the 14.5% per annum gross rate is compounded annually.
Required:
i) Calculate the size of each fund at the end of the five years. (Ignore tax considerations). (8 marks)
ii) Calculate the effective annual interest rate of the bank account investment. (4 marks)
iii) Advise your client on the basis of your calculations. (2 marks)
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