Subject: QUANTITATIVE TOOLS IN BUSINESS

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QTB – MAY 2016 – L1 – SA – Q14 – Statistics

Calculate probability of specific outcomes when tossing a coin and rolling a die

If a coin and an unbiased die are tossed together, what is the probability of
obtaining a tail and a number greater than 3?

A. 0.25
B. 0.33
C. 0.35
D. 0.50
E. 0.75

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QT – May 2016 – L1 – Q7 – Mathematics of Business Finance

Construct an amortization schedule for a loan of GH¢3,000 over 12 years with an annual interest rate of 2%.

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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QT – May 2016 – L1 – Q6b – Data Collection | Measures of Central Tendency

Compute the sample mean, variance, standard deviation, covariance, and correlation for the given data.

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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QT – May 2016 – L1 – Q6a – Data Collection

Distinguish between a population and a sample, and between a statistic and a parameter.

a)
i) Distinguish between a Sample and a Population. (2 marks)
ii) Distinguish between a Statistic and a Parameter. (2 marks)

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QT – May 2016 – L1 – Q5b – Equalities and Inequalities

Solve simultaneous equations representing a word problem about total cash in GHS 10 and GHS 20 notes.

Mini has some GH¢10 notes and some GH¢20 notes. If she has 273 notes worth a total of GH¢4,370:

Required:
i) Write down the system of linear equations. (5 marks)
ii) Solve the system of linear equations. (5 marks)

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QT – May 2016 – L1 – Q5a – Mathematics of Business Finance

Calculate the total cost, average cost, and marginal cost of producing 5000 items, and determine the production level for the lowest average cost.

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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QT – May 2016 – L1 – Q4 – Probability

Determine percentages of receipts using normal distribution and calculate mean and standard deviation based on given conditions.

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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QT – May 2016 – L1 – Q3 – Probability

Calculate the probabilities of various outcomes in a card drawing scenario, including conditional probability based on drawing a red card.

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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QT – Nov 2017 – L1 – Q7b – Mathematics of Business Finance

Calculate the future value of a depreciated vehicle and the amount required in a sinking fund to replace it.

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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QT – Nov 2017 – L1 – Q7a – Mathematics of Business Finance

Determine the timeline for savings and calculate the time required to reach a target amount with compound interest.

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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QTB – MAY 2016 – L1 – SA – Q14 – Statistics

Calculate probability of specific outcomes when tossing a coin and rolling a die

If a coin and an unbiased die are tossed together, what is the probability of
obtaining a tail and a number greater than 3?

A. 0.25
B. 0.33
C. 0.35
D. 0.50
E. 0.75

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QT – May 2016 – L1 – Q7 – Mathematics of Business Finance

Construct an amortization schedule for a loan of GH¢3,000 over 12 years with an annual interest rate of 2%.

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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QT – May 2016 – L1 – Q6b – Data Collection | Measures of Central Tendency

Compute the sample mean, variance, standard deviation, covariance, and correlation for the given data.

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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QT – May 2016 – L1 – Q6a – Data Collection

Distinguish between a population and a sample, and between a statistic and a parameter.

a)
i) Distinguish between a Sample and a Population. (2 marks)
ii) Distinguish between a Statistic and a Parameter. (2 marks)

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QT – May 2016 – L1 – Q5b – Equalities and Inequalities

Solve simultaneous equations representing a word problem about total cash in GHS 10 and GHS 20 notes.

Mini has some GH¢10 notes and some GH¢20 notes. If she has 273 notes worth a total of GH¢4,370:

Required:
i) Write down the system of linear equations. (5 marks)
ii) Solve the system of linear equations. (5 marks)

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QT – May 2016 – L1 – Q5a – Mathematics of Business Finance

Calculate the total cost, average cost, and marginal cost of producing 5000 items, and determine the production level for the lowest average cost.

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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QT – May 2016 – L1 – Q4 – Probability

Determine percentages of receipts using normal distribution and calculate mean and standard deviation based on given conditions.

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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QT – May 2016 – L1 – Q3 – Probability

Calculate the probabilities of various outcomes in a card drawing scenario, including conditional probability based on drawing a red card.

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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QT – Nov 2017 – L1 – Q7b – Mathematics of Business Finance

Calculate the future value of a depreciated vehicle and the amount required in a sinking fund to replace it.

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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QT – Nov 2017 – L1 – Q7a – Mathematics of Business Finance

Determine the timeline for savings and calculate the time required to reach a target amount with compound interest.

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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