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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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1 Layla invests AED 4,000 in an account that pays a nominal annual interest rate of 6%, compounded monthly. Calculate the value of her investment after 3 years, giving your answer to the nearest AED. ✓ Reviewed Paper 1 style Easy 3 marks Calculator + 2 Marking analysis: A learner attempts the following task: “Layla invests AED 4,000 in an account that pays a nominal annual interest rate of 6%, compounded monthly. Calculate the value of her investment after 3 years, giving your answer to the nearest AED.” Their response addresses only this point: “Identifies n = 36 (monthly compounding over 3 years).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Easy 3 marks Calculator + 7 Samir invests AED 5,000 for 4 years. Option A pays simple interest at 5% per year. Option B pays compound interest at 5% per year, compounded annually. Calculate the value of each option after 4 years, and state which option gives the greater return. ✓ Reviewed Paper 1 style Easy 3 marks Calculator + 8 Marking analysis: A learner attempts the following task: “Samir invests AED 5,000 for 4 years. Option A pays simple interest at 5% per year. Option B pays compound interest at 5% per year, compounded annually. Calculate the value of each option after 4 years, and state which option gives the greater return.” Their response addresses only this point: “Uses simple interest I = Prt to obtain Option A's value as AED 6,000.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Easy 3 marks Calculator + 11 Fatima deposits AED 200 at the end of each month into an account paying a nominal annual interest rate of 6%, compounded monthly. Calculate the value of her savings after 3 years. ✓ Reviewed Paper 1 style Easy 3 marks Calculator + 12 Marking analysis: A learner attempts the following task: “Fatima deposits AED 200 at the end of each month into an account paying a nominal annual interest rate of 6%, compounded monthly. Calculate the value of her savings after 3 years.” Their response addresses only this point: “Identifies this as the future value of a regular savings annuity with monthly payment AED 200 and a monthly rate of 0.5%.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Easy 3 marks Calculator + 13 A bank advertises a savings account with a nominal annual interest rate of 8%, compounded monthly. Calculate the effective annual interest rate of this account, giving your answer to 3 significant figures. ✓ Reviewed Paper 1 style Easy 2 marks Calculator + 14 Marking analysis: A learner attempts the following task: “A bank advertises a savings account with a nominal annual interest rate of 8%, compounded monthly. Calculate the effective annual interest rate of this account, giving your answer to 3 significant figures.” Their response addresses only this point: “Uses the effective rate formula (1 + nominal/m)^m − 1 with nominal = 0.08 and m = 12.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Easy 2 marks Calculator + 15 Inflation in a country is assumed to remain constant at 3% per year. A sum of AED 10,000 today is worth how much in real (today's) purchasing power in 5 years' time, assuming no other change in value? Calculate this real value, giving your answer to the nearest AED. ✓ Reviewed Paper 1 style Easy 2 marks Calculator + 16 Marking analysis: A learner attempts the following task: “Inflation in a country is assumed to remain constant at 3% per year. A sum of AED 10,000 today is worth how much in real (today's) purchasing power in 5 years' time, assuming no other change in value? Calculate this real value, giving your answer to the nearest AED.” Their response addresses only this point: “Recognises that inflation reduces purchasing power, so the real value must be discounted by the inflation rate.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Easy 2 marks Calculator + 25 Noor wants to save AED 20,000 in 5 years by making equal monthly deposits into an account paying a nominal annual interest rate of 4%, compounded monthly. Calculate the monthly deposit required. ✓ Reviewed Paper 1 style Easy 3 marks Calculator + 26 Marking analysis: A learner attempts the following task: “Noor wants to save AED 20,000 in 5 years by making equal monthly deposits into an account paying a nominal annual interest rate of 4%, compounded monthly. Calculate the monthly deposit required.” Their response addresses only this point: “Identifies this as finding the regular payment of a sinking fund with target future value AED 20,000, n = 60 months, and a monthly rate of 4%/12.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Easy 3 marks Calculator + 29 A credit card charges a nominal annual interest rate of 12%, compounded monthly, on any unpaid balance. Calculate the effective annual interest rate charged, to 3 significant figures, and comment on why this is higher than the advertised 12% rate. ✓ Reviewed Paper 1 style Easy 3 marks Calculator + 30 Marking analysis: A learner attempts the following task: “A credit card charges a nominal annual interest rate of 12%, compounded monthly, on any unpaid balance. Calculate the effective annual interest rate charged, to 3 significant figures, and comment on why this is higher than the advertised 12% rate.” Their response addresses only this point: “Uses the effective rate formula (1 + 0.12/12)^12 − 1.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Easy 3 marks Calculator + 31 Calculate the amount that must be invested today at a compound annual interest rate of 6.5% in order to have exactly AED 10,000 available in 6 years' time. ✓ Reviewed Paper 1 style Easy 3 marks Calculator + 32 Marking analysis: A learner attempts the following task: “Calculate the amount that must be invested today at a compound annual interest rate of 6.5% in order to have exactly AED 10,000 available in 6 years' time.” Their response addresses only this point: “Recognises this as a present-value problem: PV = FV ÷ (1 + r)^n.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. ✓ Reviewed Marking analysis Easy 3 marks Calculator + Self-assessed 0 / 0
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