SubjectScout
ENAR
Sign inGet matched
Get matched
← Back to interactive practice
Print questions only
IB · MATH AI SL

Mathematics: Applications & Interpretation SL

Financial mathematics — Topic 1

Name: ____________________Date: October 14, 2026
  1. 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.

    [3 marks]

    Marking points

    • Identifies n = 36 (monthly compounding over 3 years).
    • Uses the compound value formula with a monthly rate of 6%/12 = 0.5%.
    • Obtains a value of AED 4,787 (nearest AED).

    Examiner tip: On a financial GDC app, enter n as the number of compounding periods, not the number of years.

  2. 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.

    [3 marks]

    Marking points

    • Recognises credit for the stated point: Identifies n = 36 (monthly compounding over 3 years).
    • Identifies the missing requirement: Uses the compound value formula with a monthly rate of 6%/12 = 0.5%.
    • Identifies the missing requirement: Obtains a value of AED 4,787 (nearest AED).

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  3. 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.

    [4 marks]

    Marking points

    • Uses the reducing-balance model V = 90000(0.85)^n.
    • Obtains the value after 4 years as approximately AED 46,981.
    • Tests successive integer values of n (or uses logarithms) to locate when V falls below 40000.
    • States that the value first falls below AED 40,000 during year 5 (n = 5).

    Examiner tip: Reducing-balance depreciation multiplies by the same factor each year; do not subtract a constant amount.

  4. 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.

    [4 marks]

    Marking points

    • Recognises credit for the stated point: Uses the reducing-balance model V = 90000(0.85)^n.
    • Identifies the missing requirement: Obtains the value after 4 years as approximately AED 46,981.
    • Identifies the missing requirement: Tests successive integer values of n (or uses logarithms) to locate when V falls below 40000.
    • Identifies the missing requirement: States that the value first falls below AED 40,000 during year 5 (n = 5).

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  5. 5.

    A student borrows AED 12,000, 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 total amount repaid over the loan. (c) Calculate the total interest paid. (d) State how the total interest would change, without further calculation, if the loan term were extended to 3 years at the same rate.

    [6 marks]

    Marking points

    • Sets up the loan with PV = 12000, n = 24 monthly payments, and a monthly rate of 9%/12 = 0.75%.
    • Uses a financial (TVM) solver to obtain a monthly instalment of approximately AED 548.
    • Calculates the total repaid as 548 × 24 ≈ AED 13,152.
    • Calculates total interest as total repaid − 12000 ≈ AED 1,152.
    • Recognises that extending the term reduces the monthly instalment but increases the number of payments made.
    • States that the total interest paid would increase, because interest continues to accrue over a longer repayment period.

    Examiner tip: Keep cash-flow signs consistent in the TVM solver: the amount borrowed and the payments made must have opposite signs.

  6. 6.

    Marking analysis: A learner attempts the following task: “A student borrows AED 12,000, 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 total amount repaid over the loan. (c) Calculate the total interest paid. (d) State how the total interest would change, without further calculation, if the loan term were extended to 3 years at the same rate.” Their response addresses only this point: “Sets up the loan with PV = 12000, n = 24 monthly payments, and a monthly rate of 9%/12 = 0.75%.” Evaluate the response against the complete 6-mark task. Identify what earns credit and state every additional requirement needed for full marks.

    [6 marks]

    Marking points

    • Recognises credit for the stated point: Sets up the loan with PV = 12000, n = 24 monthly payments, and a monthly rate of 9%/12 = 0.75%.
    • Identifies the missing requirement: Uses a financial (TVM) solver to obtain a monthly instalment of approximately AED 548.
    • Identifies the missing requirement: Calculates the total repaid as 548 × 24 ≈ AED 13,152.
    • Identifies the missing requirement: Calculates total interest as total repaid − 12000 ≈ AED 1,152.
    • Identifies the missing requirement: Recognises that extending the term reduces the monthly instalment but increases the number of payments made.
    • Identifies the missing requirement: States that the total interest paid would increase, because interest continues to accrue over a longer repayment period.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  7. 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.

    [3 marks]

    Marking points

    • Uses simple interest I = Prt to obtain Option A's value as AED 6,000.
    • Uses the compound value formula to obtain Option B's value as approximately AED 6,077.53.
    • States that Option B gives the greater return.

    Examiner tip: Simple interest grows by the same fixed amount every year; compound interest grows by an increasing amount, so compound interest always overtakes simple interest at the same rate over time.

  8. 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.

    [3 marks]

    Marking points

    • Recognises credit for the stated point: Uses simple interest I = Prt to obtain Option A's value as AED 6,000.
    • Identifies the missing requirement: Uses the compound value formula to obtain Option B's value as approximately AED 6,077.53.
    • Identifies the missing requirement: States that Option B gives the greater return.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  9. 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.

    [4 marks]

    Marking points

    • Sets up PV = 8000, n = 24, monthly rate = 9%/12 = 0.75%.
    • Uses a TVM solver to obtain a monthly instalment of approximately AED 365.48.
    • Calculates the first month's interest as 8000 × 0.0075 = AED 60.00.
    • Calculates the principal portion of the first instalment as 365.48 − 60.00 ≈ AED 305.48.

    Examiner tip: In the first instalment of any loan, interest is calculated on the full original balance; only the remainder of the payment reduces the principal.

  10. 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.

    [4 marks]

    Marking points

    • Recognises credit for the stated point: Sets up PV = 8000, n = 24, monthly rate = 9%/12 = 0.75%.
    • Identifies the missing requirement: Uses a TVM solver to obtain a monthly instalment of approximately AED 365.48.
    • Identifies the missing requirement: Calculates the first month's interest as 8000 × 0.0075 = AED 60.00.
    • Identifies the missing requirement: Calculates the principal portion of the first instalment as 365.48 − 60.00 ≈ AED 305.48.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  11. 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.

    [3 marks]

    Marking points

    • Identifies this as the future value of a regular savings annuity with monthly payment AED 200 and a monthly rate of 0.5%.
    • Uses a financial solver (or the annuity formula) with n = 36 payments.
    • Obtains a final value of approximately AED 7,867.22.

    Examiner tip: A series of regular deposits is an annuity, not a single lump sum — use your GDC's annuity/TVM solver with the correct number of payments.

  12. 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.

    [3 marks]

    Marking points

    • Recognises credit for the stated point: Identifies this as the future value of a regular savings annuity with monthly payment AED 200 and a monthly rate of 0.5%.
    • Identifies the missing requirement: Uses a financial solver (or the annuity formula) with n = 36 payments.
    • Identifies the missing requirement: Obtains a final value of approximately AED 7,867.22.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  13. 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.

    [2 marks]

    Marking points

    • Uses the effective rate formula (1 + nominal/m)^m − 1 with nominal = 0.08 and m = 12.
    • Obtains an effective annual rate of approximately 8.30%.

    Examiner tip: The effective annual rate is always slightly higher than the nominal rate whenever compounding happens more than once a year.

  14. 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.

    [2 marks]

    Marking points

    • Recognises credit for the stated point: Uses the effective rate formula (1 + nominal/m)^m − 1 with nominal = 0.08 and m = 12.
    • Identifies the missing requirement: Obtains an effective annual rate of approximately 8.30%.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  15. 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.

    [2 marks]

    Marking points

    • Recognises that inflation reduces purchasing power, so the real value must be discounted by the inflation rate.
    • Divides by (1.03)^5 to obtain a real value of approximately AED 8,626.

    Examiner tip: Finding a 'real' value under inflation uses the same discounting idea as finding a present value — divide by the growth factor.

  16. 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.

    [2 marks]

    Marking points

    • Recognises credit for the stated point: Recognises that inflation reduces purchasing power, so the real value must be discounted by the inflation rate.
    • Identifies the missing requirement: Divides by (1.03)^5 to obtain a real value of approximately AED 8,626.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  17. 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.

    [4 marks]

    Marking points

    • Sets up PV = 15000, n = 36, monthly rate = 7.2%/12 = 0.6%.
    • Uses a TVM solver to obtain a monthly instalment of approximately AED 464.53.
    • Uses the amortisation (or balance) function on the GDC, or the balance formula, with k = 12 payments made.
    • Obtains an outstanding balance of approximately AED 10,354.

    Examiner tip: Most GDC financial apps have a built-in 'balance' or 'amortisation' function — use it directly rather than resumming individual payments by hand.

  18. 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.

    [4 marks]

    Marking points

    • Recognises credit for the stated point: Sets up PV = 15000, n = 36, monthly rate = 7.2%/12 = 0.6%.
    • Identifies the missing requirement: Uses a TVM solver to obtain a monthly instalment of approximately AED 464.53.
    • Identifies the missing requirement: Uses the amortisation (or balance) function on the GDC, or the balance formula, with k = 12 payments made.
    • Identifies the missing requirement: Obtains an outstanding balance of approximately AED 10,354.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  19. 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).

    [4 marks]

    Marking points

    • Sets up the equation 2 = (1.06)^n.
    • Takes logarithms of both sides and solves for n = ln(2)/ln(1.06).
    • Obtains n ≈ 11.90 years.
    • Compares this to the rule-of-72 estimate of 72 ÷ 6 = 12 years, noting the two values are very close.

    Examiner tip: The rule of 72 is a quick estimate, not an exact method — always use logarithms when an exact answer is required.

  20. 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.

    [4 marks]

    Marking points

    • Recognises credit for the stated point: Sets up the equation 2 = (1.06)^n.
    • Identifies the missing requirement: Takes logarithms of both sides and solves for n = ln(2)/ln(1.06).
    • Identifies the missing requirement: Obtains n ≈ 11.90 years.
    • Identifies the missing requirement: Compares this to the rule-of-72 estimate of 72 ÷ 6 = 12 years, noting the two values are very close.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  21. 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.

    [4 marks]

    Marking points

    • Uses annual compounding to obtain a value of approximately AED 3,828.84.
    • Uses monthly compounding (rate 5%/12, n = 60) to obtain a value of approximately AED 3,850.08.
    • States that monthly compounding gives the greater return.
    • Explains that more frequent compounding means interest is added to the balance sooner, so it starts earning its own interest earlier.

    Examiner tip: For the same nominal rate, more frequent compounding always produces a greater or equal final value — never a smaller one.

  22. 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.

    [4 marks]

    Marking points

    • Recognises credit for the stated point: Uses annual compounding to obtain a value of approximately AED 3,828.84.
    • Identifies the missing requirement: Uses monthly compounding (rate 5%/12, n = 60) to obtain a value of approximately AED 3,850.08.
    • Identifies the missing requirement: States that monthly compounding gives the greater return.
    • Identifies the missing requirement: Explains that more frequent compounding means interest is added to the balance sooner, so it starts earning its own interest earlier.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  23. 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.

    [5 marks]

    Marking points

    • Calculates the annual straight-line depreciation as (50000 − 5000) ÷ 10 = AED 4,500.
    • Obtains a straight-line value after 3 years of 50000 − 3(4500) = AED 36,500.
    • Uses V = 50000(0.85)^3 for the reducing-balance method.
    • Obtains a reducing-balance value after 3 years of approximately AED 30,706.
    • States that the reducing-balance method gives the lower value after 3 years.

    Examiner tip: Reducing-balance depreciation is fastest in the early years, since it is always a percentage of the current (not original) value.

  24. 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.

    [5 marks]

    Marking points

    • Recognises credit for the stated point: Calculates the annual straight-line depreciation as (50000 − 5000) ÷ 10 = AED 4,500.
    • Identifies the missing requirement: Obtains a straight-line value after 3 years of 50000 − 3(4500) = AED 36,500.
    • Identifies the missing requirement: Uses V = 50000(0.85)^3 for the reducing-balance method.
    • Identifies the missing requirement: Obtains a reducing-balance value after 3 years of approximately AED 30,706.
    • Identifies the missing requirement: States that the reducing-balance method gives the lower value after 3 years.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  25. 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.

    [3 marks]

    Marking points

    • 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.
    • Uses a financial solver with the correct values.
    • Obtains a required monthly deposit of approximately AED 301.66.

    Examiner tip: This is the reverse of a usual savings problem: here the final value is known and the regular payment is the unknown being solved for.

  26. 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.

    [3 marks]

    Marking points

    • Recognises credit for the stated 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.
    • Identifies the missing requirement: Uses a financial solver with the correct values.
    • Identifies the missing requirement: Obtains a required monthly deposit of approximately AED 301.66.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  27. 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.

    [4 marks]

    Marking points

    • Multiplies 1000 × 3.67 to obtain AED 3,670 before commission.
    • Calculates the commission as 2% of AED 3,670 = AED 73.40.
    • Subtracts the commission to obtain AED 3,596.60.
    • Confirms this equals 3670 × 0.98 as a check.

    Examiner tip: Apply the exchange rate first, then apply the commission to the converted amount — not to the original foreign-currency amount.

  28. 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.

    [4 marks]

    Marking points

    • Recognises credit for the stated point: Multiplies 1000 × 3.67 to obtain AED 3,670 before commission.
    • Identifies the missing requirement: Calculates the commission as 2% of AED 3,670 = AED 73.40.
    • Identifies the missing requirement: Subtracts the commission to obtain AED 3,596.60.
    • Identifies the missing requirement: Confirms this equals 3670 × 0.98 as a check.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  29. 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.

    [3 marks]

    Marking points

    • Uses the effective rate formula (1 + 0.12/12)^12 − 1.
    • Obtains an effective annual rate of approximately 12.7%.
    • Comments that monthly compounding means unpaid interest itself starts earning interest within the year, raising the true annual cost above the nominal rate.

    Examiner tip: The gap between nominal and effective rate grows both with a higher nominal rate and with more frequent compounding.

  30. 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.

    [3 marks]

    Marking points

    • Recognises credit for the stated point: Uses the effective rate formula (1 + 0.12/12)^12 − 1.
    • Identifies the missing requirement: Obtains an effective annual rate of approximately 12.7%.
    • Identifies the missing requirement: Comments that monthly compounding means unpaid interest itself starts earning interest within the year, raising the true annual cost above the nominal rate.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

  31. 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.

    [3 marks]

    Marking points

    • Recognises this as a present-value problem: PV = FV ÷ (1 + r)^n.
    • Substitutes FV = 10000, r = 0.065, n = 6.
    • Obtains a required present investment of approximately AED 6,853.

    Examiner tip: Finding a present value is simply compound growth worked backwards — divide by the growth factor instead of multiplying.

  32. 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.

    [3 marks]

    Marking points

    • Recognises credit for the stated point: Recognises this as a present-value problem: PV = FV ÷ (1 + r)^n.
    • Identifies the missing requirement: Substitutes FV = 10000, r = 0.065, n = 6.
    • Identifies the missing requirement: Obtains a required present investment of approximately AED 6,853.

    Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.

Original, unofficial practice questions from SubjectScout — not official past-paper questions.