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Financial mathematics Compound interest, reducing-balance depreciation and loan amortisation.
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Mathematics: Applications & Interpretation SL Financial mathematics
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3 A delivery van bought for AED 90,000 depreciates at 15% per year using the reducing-balance method. Find its value after 4 complete years, and state the first complete year in which its value falls below AED 40,000. ✓ Reviewed Paper 1 style Medium 4 marks Calculator + 4 Marking analysis: A learner attempts the following task: “A delivery van bought for AED 90,000 depreciates at 15% per year using the reducing-balance method. Find its value after 4 complete years, and state the first complete year in which its value falls below AED 40,000.” Their response addresses only this point: “Uses the reducing-balance model V = 90000(0.85)^n.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Medium 4 marks Calculator + 9 A family borrows AED 8,000 to be repaid by equal monthly instalments over 2 years at a nominal annual interest rate of 9%, compounded monthly. (a) Calculate the monthly instalment. (b) Calculate the amount of the first instalment that is interest. (c) Calculate the amount of the first instalment that repays the principal. ✓ Reviewed Paper 2 style Medium 4 marks Calculator + 10 Marking analysis: A learner attempts the following task: “A family borrows AED 8,000 to be repaid by equal monthly instalments over 2 years at a nominal annual interest rate of 9%, compounded monthly. (a) Calculate the monthly instalment. (b) Calculate the amount of the first instalment that is interest. (c) Calculate the amount of the first instalment that repays the principal.” Their response addresses only this point: “Sets up PV = 8000, n = 24, monthly rate = 9%/12 = 0.75%.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Medium 4 marks Calculator + 17 A loan of AED 15,000 is to be repaid over 3 years by equal monthly instalments at a nominal annual interest rate of 7.2%, compounded monthly. (a) Calculate the monthly instalment. (b) Calculate the outstanding balance immediately after the 12th payment has been made. ✓ Reviewed Paper 2 style Medium 4 marks Calculator + 18 Marking analysis: A learner attempts the following task: “A loan of AED 15,000 is to be repaid over 3 years by equal monthly instalments at a nominal annual interest rate of 7.2%, compounded monthly. (a) Calculate the monthly instalment. (b) Calculate the outstanding balance immediately after the 12th payment has been made.” Their response addresses only this point: “Sets up PV = 15000, n = 36, monthly rate = 7.2%/12 = 0.6%.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Medium 4 marks Calculator + 19 An investment of AED 4,000 grows at a constant compound annual interest rate of 6%. (a) Use logarithms to find the exact number of years required for the investment to double in value. (b) Compare your answer to the estimate given by the 'rule of 72' (72 ÷ interest rate as a percentage). ✓ Reviewed Paper 1 style Medium 4 marks Calculator + 20 Marking analysis: A learner attempts the following task: “An investment of AED 4,000 grows at a constant compound annual interest rate of 6%. (a) Use logarithms to find the exact number of years required for the investment to double in value. (b) Compare your answer to the estimate given by the 'rule of 72' (72 ÷ interest rate as a percentage).” Their response addresses only this point: “Sets up the equation 2 = (1.06)^n.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Medium 4 marks Calculator + 21 AED 3,000 is invested for 5 years at a nominal annual rate of 5%. Calculate the final value of the investment if interest is compounded (a) annually and (b) monthly. (c) State which compounding frequency gives the greater return, and explain why. ✓ Reviewed Paper 2 style Medium 4 marks Calculator + 22 Marking analysis: A learner attempts the following task: “AED 3,000 is invested for 5 years at a nominal annual rate of 5%. Calculate the final value of the investment if interest is compounded (a) annually and (b) monthly. (c) State which compounding frequency gives the greater return, and explain why.” Their response addresses only this point: “Uses annual compounding to obtain a value of approximately AED 3,828.84.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Medium 4 marks Calculator + 23 A company buys machinery for AED 50,000, expected to have a salvage value of AED 5,000 after 10 years. (a) Using the straight-line method, calculate the machinery's value after 3 years. (b) Using the reducing-balance method with an annual depreciation rate of 15%, calculate the machinery's value after 3 years. (c) State which method gives a lower value after 3 years. ✓ Reviewed Paper 2 style Medium 5 marks Calculator + 24 Marking analysis: A learner attempts the following task: “A company buys machinery for AED 50,000, expected to have a salvage value of AED 5,000 after 10 years. (a) Using the straight-line method, calculate the machinery's value after 3 years. (b) Using the reducing-balance method with an annual depreciation rate of 15%, calculate the machinery's value after 3 years. (c) State which method gives a lower value after 3 years.” Their response addresses only this point: “Calculates the annual straight-line depreciation as (50000 − 5000) ÷ 10 = AED 4,500.” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Medium 5 marks Calculator + 27 A tourist exchanges USD 1,000 for UAE dirhams at a rate of 1 USD = 3.67 AED. The exchange office charges a 2% commission on the converted amount. (a) Calculate the amount in AED before commission. (b) Calculate the amount the tourist actually receives after commission. ✓ Reviewed Paper 1 style Medium 4 marks Calculator + 28 Marking analysis: A learner attempts the following task: “A tourist exchanges USD 1,000 for UAE dirhams at a rate of 1 USD = 3.67 AED. The exchange office charges a 2% commission on the converted amount. (a) Calculate the amount in AED before commission. (b) Calculate the amount the tourist actually receives after commission.” Their response addresses only this point: “Multiplies 1000 × 3.67 to obtain AED 3,670 before commission.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Medium 4 marks Calculator + Self-assessed 0 / 0
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