Topic: Simple interest and compound interest

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  • 10 Marks

FM – May 2020 – L2 – Q3a – Simple interest and compound interest

Calculate the quarterly loan installment and prepare an amortization schedule for a loan with compound interest and equal quarterly payments.

Odapagyan Foods Ltd is borrowing GH¢500,000 to finance a project involving an expansion of its existing factory. It has obtained an offer from Sika Bank. The terms of the loan facility are as follows:

  • Annual interest rate: 22%
  • Duration: 2 years
  • Interest method: compound interest with quarterly compounding
  • Payment plan: equal installments at the end of each quarter

Required:

i) Compute the quarterly installment.
(3 marks)

ii) Prepare a loan amortization schedule to show the periodic interest charges, installment payments, principal payments, and balance of the loan at the end of each quarter.
(7 marks)

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  • 20 Marks

FM – July 2023 – L2 – Q3 – Discounted cash flow | Simple interest and compound interest

Compute the maturity value of a loan, determine the size of quarterly sinking fund deposits, and compare annuity due with ordinary annuity.

a) Osiadan Contractors Ltd plans to construct housing units in the Kpone-Katamanso District of Ghana for sale to young professionals. It has obtained a US$4 million loan facility from the International Finance Corporation (IFC). The total principal granted will be released in two equal tranches: the first tranche to be released now and the second tranche at the beginning of the fourth year. Interest will be charged on the loan at 12% per annum with semi-annual compounding. The total principal granted plus the total interest is to be paid at the end of the duration of the loan in six years’ time.

To raise money toward the settlement of the maturity value of the loan, Osiadan Contractors Ltd plans to establish a sinking fund by which it will deposit equal amounts of U.S. dollars at the beginning of every quarter starting from the third year until the end of the loan duration. The dollar deposits will be invested at 8% per annum with quarterly compounding.

Required:
i) Compute the maturity value of the loan at the end of six years. (3 marks)
ii) Compute the size of the quarterly deposits to be invested in the sinking fund to raise the amount needed to settle the maturity value of the loan. (4 marks)
iii) Compare and contrast annuity due and ordinary annuity. (3 marks)

b) Klessy Beverages Inc (Klessy), an American malt drink producer, imports barley from Australia and pays for the import in Australian dollars. It has bought a consignment of barley with an invoice value of AUD2.5 million, and payment is due next month. The exchange rate between the United States dollar (USD) and the Australian dollar (AUD) is currently trading at USD0.7265/AUD. The Managers of Klessy fear that the Australian dollar may strengthen against the US dollar. The Treasury Manager has recommended using currency options to address the potential currency risk.

Below are the CME Group’s quotations for weekly options on the Australian dollar:

Contract Specification Call Put
Contract size AUD100,000 AUD100,000
Premium (US$) 0.0131 0.0031
Strike price (US$) 0.7275 0.7275
Expiration Week 4 Week 4

Required:
i) Justify which option Klessy should buy considering its underlying currency exposure. (3 marks)
ii) Compute the intrinsic value of your selected option and interpret the results. (4 marks)
iii) Distinguish between option premium and option strike (or exercise) price. (3 marks)

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  • 4 Marks

FM – March 2023 – L2 – Q3b – Simple interest and compound interest

Determine the length of time required to double an investment of GH¢100,000 at an annual interest rate of 15%.

Trimpo Ltd can invest funds in Ghana’s financial market at 15% per annum. Presently, the Treasury Manager of the company is considering investing GH¢100,000.

Required:
Determine the length of time it will take to double the investment (round your answer to the nearest year). (4 marks)

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  • 10 Marks

FM – April 2022 – L2 – Q3a – Simple interest and compound interest

Compute the terminal value of investments in Treasury bills and fixed deposits over a five-year period and analyze the investment strategy.

An online university is setting up an endowment fund for the financing of scholarship grants. A total of GH¢200 million has been raised through fundraising events. This amount will be invested continuously for 5 years before disbursements will be made from the fund. The Trustees of the Endowment Fund have received a tentative investment strategy from the appointed Investment Manager.

Below is an extract from the tentative investment strategy:

“The seed money will be invested in fixed-income securities and negotiated short-term investments to secure the protection of the principal while earning stable returns over the 5-year gestation period. To achieve this objective, the seed money will be invested as follows: 60% in Government of Ghana 91-day Treasury Bills, 40% in 6-month fixed deposit accounts with top-class universal banks in Ghana. Over the 5-year gestation period, the maturity value of each round of investment will be rolled over as they mature.”

Being the only Trustee with expertise in finance, your fellow Trustees have asked you to do some simulations to inform them about the growth of the fund in the gestation period based on the tentative investment strategy.

Required:
i) Suppose the annual nominal interest rate on the Government of Ghana 91-day Treasury bills will be 15.2514% in year 1, 15.4814% in year 2, 15.7565% in year 3, 15.9478% in year 4, and 16.2146% in year 5. Compute the terminal value of that component of the investment at the end of the fifth year. (5 marks)
ii) Suppose the average nominal interest rate on the fixed deposits will be 16.5% over the next five years. Compute the terminal value of that component of the investment at the end of the fifth year. (3 marks)
iii) Considering the proposed strategy that the maturity value of each round of investment is rolled over as they mature, explain whether the interest that would accrue on the investment over the entire investment period would effectively be a simple interest. (2 marks)

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  • 4 Marks

FM – Nov 2019 – L2 – Q3a – Simple interest and compound interest

Calculate the balance of an endowment fund at the end of three years with varying annual interest rates.

Joy Mummy Ltd is establishing an endowment fund to finance a scholarship scheme to provide funding for the education of children of its employees. The company plans to make an initial deposit of GH¢500,000 into the fund now. The initial deposit will be invested for three years before any disbursements will be made from the fund. The effective annual rate of return on the fund is expected to be 14% in the first year, 15% in the second year, and 16.5% in the third year.

Required:
Compute the balance of the fund at the end of three years. (4 marks)

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  • 10 Marks

FM – May 2020 – L2 – Q3a – Simple interest and compound interest

Calculate the quarterly loan installment and prepare an amortization schedule for a loan with compound interest and equal quarterly payments.

Odapagyan Foods Ltd is borrowing GH¢500,000 to finance a project involving an expansion of its existing factory. It has obtained an offer from Sika Bank. The terms of the loan facility are as follows:

  • Annual interest rate: 22%
  • Duration: 2 years
  • Interest method: compound interest with quarterly compounding
  • Payment plan: equal installments at the end of each quarter

Required:

i) Compute the quarterly installment.
(3 marks)

ii) Prepare a loan amortization schedule to show the periodic interest charges, installment payments, principal payments, and balance of the loan at the end of each quarter.
(7 marks)

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  • 20 Marks

FM – July 2023 – L2 – Q3 – Discounted cash flow | Simple interest and compound interest

Compute the maturity value of a loan, determine the size of quarterly sinking fund deposits, and compare annuity due with ordinary annuity.

a) Osiadan Contractors Ltd plans to construct housing units in the Kpone-Katamanso District of Ghana for sale to young professionals. It has obtained a US$4 million loan facility from the International Finance Corporation (IFC). The total principal granted will be released in two equal tranches: the first tranche to be released now and the second tranche at the beginning of the fourth year. Interest will be charged on the loan at 12% per annum with semi-annual compounding. The total principal granted plus the total interest is to be paid at the end of the duration of the loan in six years’ time.

To raise money toward the settlement of the maturity value of the loan, Osiadan Contractors Ltd plans to establish a sinking fund by which it will deposit equal amounts of U.S. dollars at the beginning of every quarter starting from the third year until the end of the loan duration. The dollar deposits will be invested at 8% per annum with quarterly compounding.

Required:
i) Compute the maturity value of the loan at the end of six years. (3 marks)
ii) Compute the size of the quarterly deposits to be invested in the sinking fund to raise the amount needed to settle the maturity value of the loan. (4 marks)
iii) Compare and contrast annuity due and ordinary annuity. (3 marks)

b) Klessy Beverages Inc (Klessy), an American malt drink producer, imports barley from Australia and pays for the import in Australian dollars. It has bought a consignment of barley with an invoice value of AUD2.5 million, and payment is due next month. The exchange rate between the United States dollar (USD) and the Australian dollar (AUD) is currently trading at USD0.7265/AUD. The Managers of Klessy fear that the Australian dollar may strengthen against the US dollar. The Treasury Manager has recommended using currency options to address the potential currency risk.

Below are the CME Group’s quotations for weekly options on the Australian dollar:

Contract Specification Call Put
Contract size AUD100,000 AUD100,000
Premium (US$) 0.0131 0.0031
Strike price (US$) 0.7275 0.7275
Expiration Week 4 Week 4

Required:
i) Justify which option Klessy should buy considering its underlying currency exposure. (3 marks)
ii) Compute the intrinsic value of your selected option and interpret the results. (4 marks)
iii) Distinguish between option premium and option strike (or exercise) price. (3 marks)

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  • 4 Marks

FM – March 2023 – L2 – Q3b – Simple interest and compound interest

Determine the length of time required to double an investment of GH¢100,000 at an annual interest rate of 15%.

Trimpo Ltd can invest funds in Ghana’s financial market at 15% per annum. Presently, the Treasury Manager of the company is considering investing GH¢100,000.

Required:
Determine the length of time it will take to double the investment (round your answer to the nearest year). (4 marks)

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  • 10 Marks

FM – April 2022 – L2 – Q3a – Simple interest and compound interest

Compute the terminal value of investments in Treasury bills and fixed deposits over a five-year period and analyze the investment strategy.

An online university is setting up an endowment fund for the financing of scholarship grants. A total of GH¢200 million has been raised through fundraising events. This amount will be invested continuously for 5 years before disbursements will be made from the fund. The Trustees of the Endowment Fund have received a tentative investment strategy from the appointed Investment Manager.

Below is an extract from the tentative investment strategy:

“The seed money will be invested in fixed-income securities and negotiated short-term investments to secure the protection of the principal while earning stable returns over the 5-year gestation period. To achieve this objective, the seed money will be invested as follows: 60% in Government of Ghana 91-day Treasury Bills, 40% in 6-month fixed deposit accounts with top-class universal banks in Ghana. Over the 5-year gestation period, the maturity value of each round of investment will be rolled over as they mature.”

Being the only Trustee with expertise in finance, your fellow Trustees have asked you to do some simulations to inform them about the growth of the fund in the gestation period based on the tentative investment strategy.

Required:
i) Suppose the annual nominal interest rate on the Government of Ghana 91-day Treasury bills will be 15.2514% in year 1, 15.4814% in year 2, 15.7565% in year 3, 15.9478% in year 4, and 16.2146% in year 5. Compute the terminal value of that component of the investment at the end of the fifth year. (5 marks)
ii) Suppose the average nominal interest rate on the fixed deposits will be 16.5% over the next five years. Compute the terminal value of that component of the investment at the end of the fifth year. (3 marks)
iii) Considering the proposed strategy that the maturity value of each round of investment is rolled over as they mature, explain whether the interest that would accrue on the investment over the entire investment period would effectively be a simple interest. (2 marks)

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  • 4 Marks

FM – Nov 2019 – L2 – Q3a – Simple interest and compound interest

Calculate the balance of an endowment fund at the end of three years with varying annual interest rates.

Joy Mummy Ltd is establishing an endowment fund to finance a scholarship scheme to provide funding for the education of children of its employees. The company plans to make an initial deposit of GH¢500,000 into the fund now. The initial deposit will be invested for three years before any disbursements will be made from the fund. The effective annual rate of return on the fund is expected to be 14% in the first year, 15% in the second year, and 16.5% in the third year.

Required:
Compute the balance of the fund at the end of three years. (4 marks)

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