percentages.co.uk

Compound Interest Worksheet

GCSE | Years 9-11GCSE20 questions

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

Formula

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

Compound depreciation: A = P(1 − r/100)^n

Where: P = principal (starting amount), r = annual interest rate (%), n = number of years, A = final amount

Show full working for each question. Give monetary answers to the nearest penny unless stated otherwise.

  1. 1. £1,000 is invested at 5% compound interest per year for 2 years. Find the total amount.

  2. 2. £2,000 is invested at 4% compound interest for 3 years. Find the total amount.

  3. 3. £500 is invested at 3% compound interest for 2 years. Find the interest earned (not the total amount).

  4. 4. A car worth £14,000 depreciates at 20% per year. Find its value after 2 years.

  5. 5. £800 is invested at 6% compound interest for 3 years. Find the total amount.

  6. 6. A machine worth £25,000 depreciates at 15% per year for 3 years. Find its value to the nearest penny.

  7. 7. £3,500 is invested at 2.5% compound interest for 4 years. Find the total amount to the nearest penny.

  8. 8. Compare: £5,000 at 4% simple interest for 3 years versus £5,000 at 4% compound interest for 3 years. Which gives more and by how much?

  9. 9. A house is worth £220,000. It increases in value at 3.5% per year. Find its value after 5 years to the nearest pound.

  10. 10. A car worth £18,000 depreciates at 12% per year. What is it worth after 3 years to the nearest pound?

  11. 11. £4,000 is invested at 5% compound interest. After how many complete years does the total amount first exceed £5,000? Use trial and improvement.

  12. 12. £10,000 is invested at 3% compound interest for 10 years. Find the total amount to the nearest penny.

  13. 13. A laptop costs £1,200. It loses 30% of its value in year 1 and then a further 20% of its value in year 2. Find its value after 2 years.

  14. 14. £2,000 is invested at 4.5% compound interest per year. Find the interest earned in the third year alone.

  15. 15. A population of 5,000 grows at 2% per year compound. Find the population after 4 years. Give your answer to the nearest whole number.

  16. 16. £8,000 is split equally between two accounts. Account A pays 5% compound interest per year. Account B pays 6% simple interest per year. Which account has more money after 3 years, and by how much?

  17. 17. A car is worth £22,000. It depreciates at 18% per year. After how many complete years will it be worth less than £10,000? Show your working year by year.

  18. 18. An investment doubles when compound interest at 7% is applied. Approximately how many complete years does this take? Use trial and improvement.

  19. 19. £15,000 is invested at r% compound interest per year. After 2 years it is worth £16,224. Find r.

  20. 20. In 2010, House A was worth £200,000 and increased in value at 4% per year compound. House B was worth £250,000 and fell in value at 2% per year compound. In which year did House A's value first exceed House B's value?

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

Worked Answers

  1. 1. Total amount = £1,102.50

    A = 1000 × 1.05² = 1000 × 1.1025 = £1,102.50

  2. 2. Total amount = £2,249.73

    A = 2000 × 1.04³ = 2000 × 1.124864 = £2,249.73 (to the nearest penny)

  3. 3. Interest earned = £30.45

    A = 500 × 1.03² = 500 × 1.0609 = £530.45. Interest = £530.45 − £500 = £30.45

  4. 4. Value after 2 years = £8,960

    A = 14000 × 0.80² = 14000 × 0.64 = £8,960

  5. 5. Total amount = £952.81

    1.06² = 1.1236; 1.06³ = 1.1236 × 1.06 = 1.191016; A = 800 × 1.191016 = £952.81

  6. 6. Value after 3 years = £15,353.13

    0.85² = 0.7225; 0.85³ = 0.7225 × 0.85 = 0.614125; A = 25000 × 0.614125 = £15,353.13

  7. 7. Total amount = £3,863.34

    1.025² = 1.050625; 1.025&sup4; = 1.050625² = 1.103813; A = 3500 × 1.103813 = £3,863.34

  8. 8. Compound interest gives more by £24.32

    Simple: 5000 + (5000 × 4/100 × 3) = 5000 + 600 = £5,600. Compound: 5000 × 1.04³ = 5000 × 1.124864 = £5,624.32. Difference = £5,624.32 − £5,600 = £24.32

  9. 9. House value after 5 years = £261,291

    1.035¹ = 1.035; ² = 1.071225; ³ = 1.108718; &sup4; = 1.147523; &sup5; = 1.187686; A = 220000 × 1.187686 = £261,291 (to nearest pound)

  10. 10. Car value after 3 years = £12,267

    0.88² = 0.7744; 0.88³ = 0.7744 × 0.88 = 0.681472; A = 18000 × 0.681472 = £12,266.50 ≈ £12,267 (to nearest pound)

  11. 11. 5 years

    After 4 years: 4000 × 1.05&sup4; = 4000 × 1.21551 = £4,862.03 (still below £5,000). After 5 years: 4000 × 1.05&sup5; = 4000 × 1.27628 = £5,105.13 (exceeds £5,000). So 5 complete years.

  12. 12. Total amount = £13,439.16

    A = 10000 × 1.03¹&sup0; = 10000 × 1.343916 = £13,439.16

  13. 13. Value after 2 years = £672

    After year 1: 1200 × 0.70 = £840. After year 2: 840 × 0.80 = £672. (Alternatively: 1200 × 0.70 × 0.80 = 1200 × 0.56 = £672)

  14. 14. Interest in year 3 = £97.42

    End of year 2: 2000 × 1.045² = 2000 × 1.092025 = £2,184.05. End of year 3: £2,184.05 × 1.045 = £2,281.47. Interest in year 3 = £2,281.47 − £2,184.05 = £97.42

  15. 15. Population after 4 years = 5,412

    1.02&sup4; = 1.08243216; A = 5000 × 1.08243216 = 5,412.16 ≈ 5,412

  16. 16. Account B has more money after 3 years, by £89.50

    Each account receives £4,000. Account A (compound): 4000 × 1.05³ = 4000 × 1.157625 = £4,630.50. Account B (simple): 4000 + (4000 × 0.06 × 3) = 4000 + 720 = £4,720. Difference: £4,720 − £4,630.50 = £89.50

  17. 17. 4 complete years

    Year 1: 22000 × 0.82 = £18,040. Year 2: 18040 × 0.82 = £14,792.80. Year 3: 14792.80 × 0.82 = £12,130.10. Year 4: 12130.10 × 0.82 = £9,946.68. The value falls below £10,000 after 4 complete years.

  18. 18. 11 complete years

    After 10 years: 1.07¹&sup0; ≈ 1.9672 (not yet doubled). After 11 years: 1.07¹¹ ≈ 1.9672 × 1.07 ≈ 2.1049 (doubled). So 11 complete years.

  19. 19. r = 4%

    15000 × (1 + r/100)² = 16224. (1 + r/100)² = 16224 ÷ 15000 = 1.0816. 1 + r/100 = √1.0816 = 1.04. r/100 = 0.04. r = 4%

  20. 20. 2014 (after 4 years)

    After 3 years (2013): House A = 200000 × 1.04³ = 200000 × 1.124864 = £224,973. House B = 250000 × 0.98³ = 250000 × 0.941192 = £235,298. House B still leads. After 4 years (2014): House A = 200000 × 1.04&sup4; = 200000 × 1.169859 = £233,972. House B = 250000 × 0.98&sup4; = 250000 × 0.922368 = £230,592. House A exceeds House B in 2014.

Related resources

Percentage Change Calculator

Find the percentage change between two values.

GCSE Percentages Revision

Full GCSE revision guide covering all percentage topics with exam-style examples.

Simple Interest Worksheet

Simple interest practice questions with worked answers.

Compound Percentage Change Worksheet

Questions on repeated and compound percentage changes.