Topic: Mathematics of Business Finance

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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.

Question

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)

Answer

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Tags: Compound Interest, Interest calculation, Loan Repayment, Simple Interest
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

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.

Question

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?

Answer

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Tags: Algebraic Fractions, Charity Donations, Fractions, Proportional Distribution
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

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.

Question

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)

Answer

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Tags: Cost Calculation, Linear Equations, Simultaneous Equations
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

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

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

Question

The sufficient and necessary conditions for a firm that wants to minimize its operational costs

Answer

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Tags: Derivatives, Minimization, Operational Costs
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

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

Question

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

Answer

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Tags: Amortization, Interest rates, Sinking Fund
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

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

Identifies the correct definition of an annuity.

Question

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

Answer

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Tags: Annuity, Financial Commitments, Payments
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2015

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

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

Question

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

Answer

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Tags: Commission, Ice Cream Sales, Retailer Cost
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

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

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

Question

The number of units of goods produced when utilizing units of labor and 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

Answer

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Tags: Capital, Labor, Production Function
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

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

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

Question

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

Answer

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Tags: Break-Even Point, Cost Analysis, Production
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

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.

Question

Given that the Total Revenue (TR) function is:

and the Total Cost (TC) function is:

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

Answer

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Tags: Calculus, Output Level, Profit Maximization, Total Cost, Total Revenue
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2015

QT – May 2019 – L1 – Q2b – Mathematics of Business Finance

Calculate NPV and IRR for two machines and determine which machine yields a better return.

Question

BonBone Company Ltd wants to make a decision on which of the two machines to purchase. Each will involve a GH¢10,000 investment. The expected net incremental cash flows are given by the table below:

Year	Machine I (GH¢)	Machine II (GH¢)
1	5,000.00	2,000.00
2	4,000.00	3,000.00
3	2,000.00	5,000.00
4	2,000.00	4,000.00

Required:

i) If the company’s cost of capital is 10%, calculate the Net Present Value (NPV) of Machine I and Machine II and determine which machine should be purchased for higher returns. (8 marks)

ii) If the initial investment for Machine I is changed to GH¢4,000 and Machine II is changed to GH¢2,000, calculate the Internal Rate of Return (IRR) for Machine I and Machine II. (6 marks)

iii) If the IRRs in (ii) above are to be used as the basis of selection, determine which machine should be purchased for higher returns. (2 marks)

Answer

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Tags: Capital Budgeting, Discounting, Internal Rate of Return, Investment Decision, Net Present Value

Topic: Mathematics of Business Finance
Series: MAY 2019

QT – May 2019 – L1 – Q2a – Mathematics of Business Finance

Distinguish between IRR and NPV, and evaluate investment decisions using NPV and IRR.

Question

Distinguish between Internal Rate of Return and Net Present Value. (4 marks)

Answer

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Tags: Capital Budgeting, Discounting, Internal Rate of Return, Investment Decision, Net Present Value
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2019

QT – May 2017 – L1 – Q2a – Mathematics of Business Finance

Calculate the accumulated amount of an investment using compound interest.

Question

Calculate the accumulated amount if GH¢2500.00 were invested at 18% compound interest for a period of six years.

Answer

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Tags: Accumulated value, Compound Interest, Investment
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2017

QT – Nov 2016 – L1 – Q4c – Mathematics of Business Finance

Calculate the semi-annual sinking fund deposit required to repay a loan after 5 years.

Question

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)

Answer

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Tags: Compound Interest, Financial Calculations, Loan Repayment, Sinking Fund
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2016

QT – Nov 2016 – L1 – Q4b – Mathematics of Business Finance

Calculate the monthly amortization payments, total interest, and equity for a house loan at 9% interest over 25 years.

Question

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)

Answer

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Tags: Equity, Financial Calculations, Interest, Loan amortization
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2016

QT – Nov 2016 – L1 – Q4a – Mathematics of Business Finance

Explain the terms annuities, sinking fund, and amortization related to loan repayment.

Question

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)

Answer

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Tags: Amortization, Annuities, Loan Repayment, Sinking Fund
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2016

QT – May 2018 – L1 – Q5 – Mathematics of Business Finance

Calculate the size of an investment with varying interest rates, including savings accumulation, withdrawals, and future balances.

Question

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)

Answer

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Tags: Compound Interest, Investment, Time value of money
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2018

QT – May 2018 – L1 – Q1b – Mathematics of Business Finance

Calculate the loan instalment for the purchase of machinery over five years with a 9% interest rate.

Question

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)

Answer

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Tags: Instalments, Loan amortization, Loan Calculation
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2018

QT – May 2018 – L1 – Q1a – Mathematics of Business Finance

Compare returns from a bank account and savings fund with different compounding rates and calculate the effective interest rate.

Question

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)

Answer

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Tags: Compound Interest, Effective Annual Interest Rate, Investment Decision
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2018

QT – Nov 2018 – L1 – Q3b – Mathematics of Business Finance

Calculate the maximum loan Kasuli can borrow at 15% interest with monthly payments of GH¢1,400 over 20 years.

Question

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)

Answer

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Tags: Interest Rate, Loan, Monthly Payments, Mortgage, Present Value
Level: Level 1