Topic: Mathematics of Business Finance

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  • 20 Marks

QTB – Nov 2014 – L1 – SB – Q6 – Mathematics of Business Finance

Calculate the value of an investment with compound interest, the payoff amount for a loan with simple interest, and the additional interest for a loan with monthly payments and reduced interest rates.

a. If N250,000 is invested in an account that earns 4% per year compound interest, what is the:
i. value of the investment after 5 years? (3 Marks)
ii. total interest earned? (2 Marks)

b. When it was apparent that your parents could not afford to finance your university education, you sought and obtained a 4-year loan of N250,000.00 from Education Bank Limited. The bank imposed a simple interest rate of 7½%.
i. How much do you need to pay off the bank now

(4 years after) that you are through with your study?

(7 Marks)
ii. If you decide to be paying N25,000 every month from now and the bank agreed to reduce the interest rate to 1% per month on the unpaid balance at the beginning of the month, how much additional total interest will be paid? (8 Marks)

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  • 10 Marks

QTB – Nov 2014 – L1 – SB – Q1b – Mathematics of Business Finance

Determine the total sum of money the Chief Accountant of Zeesco Plc. plans to donate to 4 not-for-profit organisations, given the donations for each organisation.

The Chief Accountant of Zeesco Plc. has a large sum of money which she plans to donate to 4 not-for-profit organisations. She plans to give  of this amount to organisation A. Out of the remaining amount, she plans to give    to organisation B. Also, she intends to give           of the balance to organisation C and the rest to organisation D. If she plans to give 11 million naira to organisation D, how much does she plan to share among these organisations?

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  • 10 Marks

QTB – Nov 2014 – L1 – SB – Q1a – Mathematics of Business Finance

Determine the cost of calculators and books using a system of linear equations and solve for individual costs.

The cost of purchasing 8 calculators and 10 books is 158 (thousands of naira).
At another instance, the cost of purchasing 15 calculators and 3 books is 123 (thousands of naira).

Required:
i. Use the information above to write down a system of linear equations to describe the given cost scenario. (4 Marks)
ii. Solve the resulting system of equations. (4 Marks)
iii. Find the cost of each calculator and each book. (2 Marks)

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  • 1 Marks

QTB – Nov 2014 – L1 – SA – Q20 – Mathematics of Business Finance

Identifies the conditions necessary for a firm to minimize operational costs.

The sufficient and necessary conditions for a firm that wants to minimize its operational costs f(x)

 

 

 

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  • 1 Marks

QTB – Nov 2014 – L1 – SA – Q19 – Mathematics of Business Finance

Determines the interest rate condition for a sinking fund to have a lower periodic cost than amortization

If the interest rate received on a sinking fund is ……………….., the periodic cost for the sinking fund is lower than that for amortization.
A. Lower than that charged on the debt
B. Equal to that charged on the debt
C. Higher than that charged on the debt
D. Equal to zero
E. Equal to one

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  • 1 Marks

QTB – Nov 2014 – L1 – SA – Q18 – Mathematics of Business Finance

Identifies the correct definition of an annuity.

An annuity is defined as the:
A. Specific amount of money saved at regular intervals meant to be used in funding some future financial commitments
B. Lump sum investment designed to produce a sequence of equal regular payments over time
C. Specific amount of money received at intervals which is not necessarily equal to fund some future financial commitments
D. Lump sum investment designed to produce a sequence of unequal but regular payments over time
E. Repayment of interest-bearing debts through a series of equal regular payments until the debt is entirely paid off with the accrued interest

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  • 1 Marks

QTB – Nov 2014 – L1 – SA – Q17 – Mathematics of Business Finance

Calculates the estimated retailer’s daily cost based on sales and commission.

A retailer sells 2,000 cups of ice cream daily at Bolekaja bus stop for N250 per cup. If the retailer’s commission on each cup is 27% of the selling price, the estimated retailer’s daily cost will be:
A. N250,000
B. N285,000
C. N325,000
D. N350,000
E. N365,000

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  • 1 Marks

QTB – Nov 2014 – L1 – SA – Q16 – Mathematics of Business Finance

Calculates the number of units produced based on labor and capital input.

The number of units of goods produced when utilizing x units of labor and y units of capital is given by:

How many units of goods will be produced by using 81 units of labor and 256 units of capital?
A. 2,880
B. 2,908
C. 2,960
D. 5,360
E. 8,640

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  • 1 Marks

QTB – Nov 2014 – L1 – SA – Q15 – Mathematics of Business Finance

Determines the smallest number of units to produce for break-even.

Assume that the standard selling price of a medium-size detergent produced by BICU Nigeria Limited is N250 per unit. If the total fixed cost is N85,000 and the cost of producing each unit is N130, what is the smallest number of units which the company should produce in order to break even?
A. 709
B. 708
C. 707
D. 706
E. 700

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  • 6 Marks

QTB – Nov 2015 – L1 – SB – Q2c – Mathematics of Business Finance

Find the level of output at which profit is maximized using given revenue and cost functions.

Given that the Total Revenue (TR) function is:

a

and the Total Cost (TC) function is:

Determine the level of output at which profit is maximized. (6 Marks)

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  • 6 Marks

QTB – Nov 2015 – L1 – SB – Q2a – Mathematics of Business Finance

Calculate price elasticity of demand using given demand function and interpret the result.

Given that the demand function of a business is

calculate the price elasticity of demand when x=5  and interpret your result.

(Total: 6 Marks)

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  • 20 Marks

QTB – Nov 2015 – L1 – SB – Q1 – Mathematics of Business Finance

Calculate depreciation and salvage value of an asset using the reducing balance method.

A company buys an item having a useful life of 10 years for N1,000,000. If the company depreciates the item by the reducing balance method:

a. Determine the depreciation for the first year.
b. Estimate the depreciation for the second and third years.
c. What is the salvage value of the asset?

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  • 1 Marks

QTB – Nov 2015 – L1 – SA – Q19 – Mathematics of Business Finance

This question asks which type of loan incurs a higher effective rate if paid off ahead of time.

The borrower who pays off a …………………… ahead of time pays a higher effective rate:

A. Discounted loan
B. Standing loan
C. Amortised loan
D. Ordinary loan
E. Bank loan

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  • 1 Marks

QTB – Nov 2015 – L1 – SA – Q18 – Mathematics of Business Finance

This question identifies the term used to describe the process of calculating present value from future value.

The term used to describe the process of working backwards in time to find the present value from the future value of an investment is known as:

A. Discount
B. Discounting
C. Discount Rate
D. Annuity
E. Amortization

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  • 20 Marks

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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  • 10 Marks

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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  • 9 Marks

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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  • 11 Marks

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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  • 10 Marks

QT – Nov 2017 – L1 – Q1d – Mathematics of Business Finance

Calculate and compare the annual percentage rates for two loan repayment options.

The Asogli Company Ltd has been offered the following alternative terms for a one-year loan to be repayable plus the interest in full at the end of the year:
i) 2.5% per month compounded monthly
ii) 10% per six months compounded six-monthly.

Required:
Calculate, for each alternative, the annual percentage rate of interest. Recommend one of the alternatives and explain why.

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  • 7 Marks

QT – May 2019 – L1 – Q7b – Mathematics of Business Finance

Explain the concept of a sinking fund and calculate equal annual payments needed to accumulate a replacement fund.

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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