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NBT Quantitative Literacy: Percentages and Financial Mathematics Flashcards

6 cards from real NBT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 NBT Quantitative Literacy: Percentages and Financial Mathematics flashcards as text

  1. A car is purchased new and depreciates at 15% per year on a reducing-balance basis. After exactly 3 years, the car's book value is R4,913. What was the original purchase price of the car?

    Answer: R8,000

    Using the reducing-balance formula: Final Value = P × (1 − r)^n. Rearranging: P = 4913 ÷ (0.85)³ = 4913 ÷ 0.614125 = R8,000. A common error is dividing by 0.85 only once (giving R5,780) or multiplying instead of dividing (treating depreciation as growth).

  2. A retailer increases all clothing prices by 20% in January to cover rising costs, then offers a flat 20% discount on all items in July to clear stock. A jacket originally priced at R500 goes through both adjustments. What is its final selling price?

    Answer: R480.00

    After the 20% increase: R500 × 1.20 = R600. After the 20% discount: R600 × 0.80 = R480. The net multiplier is 1.20 × 0.80 = 0.96, a 4% net decrease — not zero. The discount is applied to the already-inflated R600, so 20% of R600 (R120) is larger than 20% of the original R500 (R100), making the net effect a loss.

  3. A laptop is advertised at R9,775 VAT inclusive. VAT is levied at 15%. What is the VAT-exclusive (pre-tax) price of the laptop?

    Answer: R8,500.00

    The VAT-inclusive price equals the pre-tax price × 1.15. Therefore: pre-tax price = R9,775 ÷ 1.15 = R8,500. The most common error (answer A) is calculating 15% of the inclusive price and subtracting it: R9,775 × 0.85 = R8,308.75 — this is incorrect because it removes 15% of the wrong base. You must divide by 1.15, not multiply by 0.85.

  4. An investor places R50,000 in a fixed deposit earning a nominal 11% per annum. Inflation over the same period is 8% per annum. Using the Fisher equation, what is the real rate of return, rounded to two decimal places?

    Answer: 2.78%

    The Fisher equation: real rate = (1 + nominal rate) ÷ (1 + inflation rate) − 1 = (1.11 ÷ 1.08) − 1 = 1.027778 − 1 ≈ 2.78%. The simple approximation (11% − 8% = 3.00%) slightly overstates the real return because it ignores the compounding interaction between inflation and the nominal rate. Answer A (3.00%) is the common approximation, not the exact Fisher result.

  5. A television set has a cash price of R6,000. Under hire purchase terms, the buyer pays a 10% deposit and then 12 monthly instalments of R530. What is the total interest paid expressed as a percentage of the original cash price?

    Answer: 16.0%

    Deposit = 10% × R6,000 = R600. Total instalments = 12 × R530 = R6,360. Total hire purchase cost = R600 + R6,360 = R6,960. Interest paid = R6,960 − R6,000 = R960. As a percentage of cash price: R960 ÷ R6,000 × 100 = 16.0%. A common error is expressing the interest as a percentage of the hire purchase total (R960 ÷ R6,960 ≈ 13.8%) rather than the cash price.

  6. A product's price increased by 10% at the end of Year 1 and by a further 15% at the end of Year 2. The price at the end of Year 2 is R1,012.50. What was the price before any increases were applied?

    Answer: R800.00

    The combined multiplier is 1.10 × 1.15 = 1.265. Therefore: original price = R1,012.50 ÷ 1.265 = R800.00. Verification: R800 × 1.10 = R880; R880 × 1.15 = R1,012. Answer A (R810) arises from incorrectly adding the rates (10% + 15% = 25%) and dividing by 1.25. Answers B and D arise from reversing only one of the two increases.