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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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Royal Driving School is considering investing in a profitable project. The school is given the following investment alternatives and percentage rates of return.
Over the past 300 days, market conditions have been moderate for 150 days and good for 60 days.
Required:
i) Calculate the expected return for each type of investment. (4 marks)
ii) Determine the optimum investment strategy for Royal Driving School. (3 marks)
b) The number of errors made by 294 students of Royal Driving School in their first attempt at a driving test is grouped in the following frequency distribution:
| Number of Errors | Number of Students |
|---|---|
| 7 – 13 | 3 |
| 14 – 20 | 12 |
| 21 – 27 | 23 |
| 28 – 34 | 44 |
| 35 – 41 | 54 |
| 42 – 48 | 56 |
| 49 – 55 | 43 |
| 56 – 62 | 24 |
| 63 – 69 | 23 |
| 70 – 76 | 12 |
Required:
i) Compute an estimate of the mean and mode for the distribution. (3 marks)
ii) Construct an ogive for the distribution. (4 marks)
iii) Using the ogive in (ii) above, estimate the median for the distribution. (3 marks)
iv) Use the ogive in (ii) above to estimate the percentage of errors within one standard deviation of the mean. (3 marks)
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Membership of Pro Amalion, a network of professional volunteers, has grown over the years but in the months of the second quarter, there was always a decline. The table below shows membership records for a period of four years:
| Year | 1st Quarter | 2nd Quarter | 3rd Quarter | 4th Quarter |
|---|---|---|---|---|
| Year 1 | 713 | 694 | 735 | 755 |
| Year 2 | 767 | 733 | 766 | 780 |
| Year 3 | 787 | 755 | 798 | 814 |
| Year 4 | 816 | 790 | 826 | 843 |
Required:
i) Calculate the centered four-quarterly moving average of membership. (4 marks)
ii) Using a least squares trend equation based on (i) above, calculate the trend values. (5 marks)
iii) Using (ii) above, calculate the percentage seasonal variation and the average seasonal variation of membership. (5 marks)
iv) Determine the seasonally adjusted forecast of membership for each of the four quarters of Year 5. (4 marks)
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Find Related Questions by Tags, levels, etc.
In a study commissioned by Ofo Stores, the researcher examined the spending habits of the residents of Kojokrom. He found the spending habits to be normally distributed with a mean of GH¢700 and a standard deviation of GH¢70.
Required:
i) Determine the probability that a resident selected at random spends:
ii) Calculate the amount:
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The normal distribution is a probability distribution which usually applies to continuous variables.
Required:
i) State FOUR (4) properties of the Normal Distribution. (4 marks)
ii) State TWO (2) examples of phenomena which closely follow a Normal Distribution. (2 marks)
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BomBo, a market researcher at a major African Automobile Company (African Moon), classified households by car ownership. The relative frequencies of households for each category of ownership are shown below:
| Number of Cars Per Household | Relative Frequencies |
|---|---|
| 0 | 0.10 |
| 1 | 0.30 |
| 2 | 0.40 |
| 3 | 0.12 |
| 4 | 0.06 |
| 5 | 0.02 |
Required:
(i) Calculate the expected value of the random variable. (4 marks)
(ii) Calculate the standard deviation of the random variable. (4 marks)
(iii) Draw a Relative Percentage Histogram for the data. (4 marks)
(iv) Using (i)-(iii), comment on the distribution of the data. (3 marks)
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Find Related Questions by Tags, levels, etc.
Kasuli, a Marketing Executive who could not recover any amount out of his investment, decided to take a mortgage at an interest rate of 15% over a 20-year term. If his income is enough to enable him to pay GH¢1,400 per month, what is the maximum amount he can borrow? (10 marks)
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Kwabena was able to recover GH¢150,000 out of GH¢200,000 invested in the Savings and Loans Company. How much money should he invest at a return of 6% per annum so as to earn an annual income of GH¢15,000 for a period of 10 years? (10 marks)
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Due to changes in market conditions, the company finds the demand qq (in thousands) for their kente strips to be 
at a price of GH¢p per kente strip.
Required:
(i) Determine the elasticity of demand when the price is GH¢5 and when the price is GH¢15 per kente strip. (6 marks)
(ii) Comment on your results in (i). (2 marks)
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