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Edexcel GCSE Higher Percentage Worksheet

Edexcel GCSE HigherHigher Tier20 questions

Free to print and use in your classroom. No sign-up required.

Formulae

Compound interest: A = P(1 + r/100)^n

Depreciation: A = P(1 − r/100)^n

Where P = starting value, r = annual rate (%), n = number of years, A = final value

All questions require a calculator. Show all working. Give monetary answers to the nearest penny unless stated otherwise. The number of marks available is shown in brackets.

  1. 1. After a 32% increase, a price is £396. Find the original price. [2 marks]

  2. 2. After a 45% reduction, a sofa costs £275. Find the original price. [2 marks]

  3. 3. A price including VAT at 20% is £252. Find the price before VAT. [2 marks]

  4. 4. Use A = P(1 + r/100)^n to find the value of £7,500 invested at 4% compound interest per year for 3 years. Give your answer to the nearest penny. [3 marks]

  5. 5. Use A = P(1 − r/100)^n to find the value of a car worth £21,000 after it depreciates at 17% per year for 3 years. Give your answer to the nearest pound. [3 marks]

  6. 6. Use A = P(1 + r/100)^n to find the value of £12,000 invested at 5.5% compound interest for 4 years. Give your answer to the nearest penny. [3 marks]

  7. 7. A car is bought for £15,000 and sold for £11,400. Calculate the percentage loss. [2 marks]

  8. 8. A jeweller buys a ring for £840 and sells it for £1,050. Calculate the percentage profit. [2 marks]

  9. 9. A house is worth £280,000. It appreciates at 3.8% per year compound. What is it worth after 5 years? Give your answer to the nearest pound. [3 marks]

  10. 10. £15,000 is invested at r% compound interest per year. After 2 years the total is £16,348.95. Use A = P(1 + r/100)^n to find r. Give your answer to 1 decimal place. [3 marks]

  11. 11. A salary rose by 8% in year 1 and by 5% in year 2. Calculate the overall percentage increase over the two years. [3 marks]

  12. 12. A population of 78,000 decreases at 2.2% per year compound. After how many complete years will it first fall below 70,000? Show your working. [4 marks]

  13. 13. After a 6.4% pay rise, a worker earns £38,296. What did they earn before the pay rise? [2 marks]

  14. 14. Leah buys a house for £230,000 and spends £12,500 on renovations. She sells the house for £272,500. Calculate the percentage profit on the total amount she spent. [3 marks]

  15. 15. An investment grows from £8,000 to £10,077.70 over 5 years with compound interest. Use A = P(1 + r/100)^n to find the annual interest rate. Give your answer to 1 decimal place. [4 marks]

  16. 16. A piece of equipment costs £45,000. It depreciates at 14% per year for 5 years. Use A = P(1 − r/100)^n to find the value after 5 years. Give your answer to the nearest pound. [3 marks]

  17. 17. A price is increased by 15% and then the new price is reduced by 15%. Show that the final price is 2.25% less than the original price and explain why the two changes do not cancel out. [3 marks]

  18. 18. Use A = P(1 + r/100)^n to find the minimum amount, to the nearest pound, that must be invested now at 3% compound interest per year so that the total is at least £20,000 after 6 years. [4 marks]

  19. 19. A van is bought for £26,000. In year 1, it depreciates at 22%. From year 2 onwards, it depreciates at 12% per year. Use A = P(1 − r/100)^n to find the value after 4 years in total. Give your answer to the nearest pound. [4 marks]

  20. 20. Two savings accounts are offered. Account P: £10,000 at 4% compound interest for 5 years. Account Q: £10,000 at 5.5% simple interest for 5 years. Find the difference in the final amounts and explain which account gives the greater return. Use A = P(1 + r/100)^n for Account P. [4 marks]

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Worked Answers

  1. 1. £300

    £396 ÷ 1.32 = £300

  2. 2. £500

    £275 ÷ 0.55 = £500

  3. 3. £210

    £252 ÷ 1.20 = £210

  4. 4. £8,436.48

    A = 7500 × (1 + 4/100)³ = 7500 × 1.04³ = 7500 × 1.124864 = £8,436.48

  5. 5. £12,048

    A = 21000 × (1 − 17/100)³ = 21000 × 0.83³; 0.83² = 0.6889; 0.83³ = 0.6889 × 0.83 = 0.571787; A = 21000 × 0.571787 = £12,007.53 ≈ £12,008

  6. 6. £14,874.80

    A = 12000 × 1.055&sup4;; 1.055² = 1.113025; 1.055&sup4; = 1.113025² = 1.238825; A = 12000 × 1.238825 = £14,865.90

  7. 7. 24%

    Loss = £15,000 − £11,400 = £3,600; percentage = £3,600 ÷ £15,000 × 100 = 24%

  8. 8. 25%

    Profit = £1,050 − £840 = £210; percentage = £210 ÷ £840 × 100 = 25%

  9. 9. £338,898

    A = 280000 × 1.038&sup5;; 1.038² = 1.077444; 1.038&sup4; = 1.077444² = 1.160885; 1.038&sup5; = 1.160885 × 1.038 = 1.204998; A = 280000 × 1.204998 = £337,399 ≈ £337,399

  10. 10. r = 4.5%

    16348.95 ÷ 15000 = 1.08993; √1.08993 = 1.04400; r = 4.4% (to 1 d.p.)

  11. 11. 13.4%

    Combined multiplier = 1.08 × 1.05 = 1.134; overall increase = 13.4%

  12. 12. After 5 complete years

    Year 1: 78000 × 0.978 = 76,284. Year 2: 76,284 × 0.978 = 74,585.8. Year 3: 74,585.8 × 0.978 = 72,944.9. Year 4: 72,944.9 × 0.978 = 71,340.3. Year 5: 71,340.3 × 0.978 = 69,790.8. Population first falls below 70,000 after 5 complete years.

  13. 13. £36,000

    £38,296 ÷ 1.064 = £36,000

  14. 14. 12.5%

    Total spent = £230,000 + £12,500 = £242,500; profit = £272,500 − £242,500 = £30,000; percentage = £30,000 ÷ £242,500 × 100 = 12.37% ≈ 12.4%

  15. 15. r = 4.7%

    10077.70 ÷ 8000 = 1.259713; 1.259713^(1/5) = 1.047; r = 4.7% (to 1 d.p.)

  16. 16. £19,987

    A = 45000 × 0.86&sup5;; 0.86² = 0.7396; 0.86&sup4; = 0.7396² = 0.547008; 0.86&sup5; = 0.547008 × 0.86 = 0.470427; A = 45000 × 0.470427 = £21,169.22

  17. 17. Final price is 2.25% less than the original

    Combined multiplier = 1.15 × 0.85 = 0.9775. So the final price is 97.75% of the original, which is 2.25% less. The changes do not cancel because the 15% decrease is applied to the already increased (higher) value, so the amount subtracted is greater than the amount added.

  18. 18. £16,743

    Need P × 1.03&sup6; ≥ 20000. 1.03² = 1.0609; 1.03&sup4; = 1.0609² = 1.126508; 1.03&sup6; = 1.126508 × 1.0609 = 1.194052. P = 20000 ÷ 1.194052 = £16,751.99 ≈ £16,752.

  19. 19. £14,151

    After year 1 (22% depreciation): 26000 × 0.78 = £20,280. Years 2, 3, 4 at 12% per year: 20280 × 0.88³; 0.88² = 0.7744; 0.88³ = 0.681472; A = 20280 × 0.681472 = £13,821.86 ≈ £13,822.

  20. 20. Account Q gives £500 more; Account P = £12,166.53; Account Q = £12,750

    Account P: A = 10000 × 1.04&sup5;; 1.04² = 1.0816; 1.04&sup4; = 1.0816² = 1.169859; 1.04&sup5; = 1.169859 × 1.04 = 1.216653; A = £12,166.53. Account Q: A = 10000 + (10000 × 5.5/100 × 5) = 10000 + 2750 = £12,750. Account Q gives £12,750 − £12,166.53 = £583.47 more than Account P.

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