GCSE Higher Percentage Worksheet
Free to print and use in your classroom. No sign-up required.
GCSE Higher Percentage Worksheet
Key formulae
Compound growth / interest: A = P × multiplier^n
Reverse percentage: Original = Final ÷ multiplier
Give monetary answers to 2 decimal places unless stated otherwise.
GCSE Higher tier percentage questions. Topics include: reverse percentages, compound interest and depreciation, repeated percentage change, and problem-solving with percentages. Show marks are given in brackets.
Section A: Reverse percentages
1. After a 20% increase, a price is £780. Find the original price. (2 marks)
2. After a 35% discount, a coat costs £91. Find the original price. (2 marks)
3. An item costs £141 including VAT at 17.5%. Find the pre-VAT price. (2 marks)
4. After a 6.5% pay rise, a salary is £38,770. Find the original salary. (2 marks)
5. A price increases by 15% and then by a further 10%. The final price is £379.50. Find the original price. (3 marks)
6. After two years of compound growth at 4% per year, an investment is worth £10,816. Find the original investment. (3 marks)
Section B: Compound interest and depreciation
7. £3,200 is invested at 4.5% compound interest per year for 3 years. Find the total amount to the nearest penny. (2 marks)
8. A car worth £18,500 depreciates at 14% per year for 3 years. Find its value to the nearest penny. (2 marks)
9. £12,000 is invested at 3.2% compound interest per year. Find the total amount after 4 years to the nearest penny. (2 marks)
10. A machine costs £45,000. It depreciates at 10% per year. After how many complete years will its value first fall below £30,000? Show your working year by year. (3 marks)
11. £5,000 is invested at r% compound interest per year. After 2 years it is worth £5,408. Find the value of r. (3 marks)
12. Compare £8,000 at 5% simple interest for 4 years with £8,000 at 5% compound interest for 4 years. Find the difference to the nearest penny. (3 marks)
13. A house is worth £240,000. It increases in value at 3% per year for 5 years. Find its value to the nearest pound. (2 marks)
Section C: Repeated and compound percentage change
14. A value increases by 10% then decreases by 10%. What is the overall percentage change? (2 marks)
15. A price increases by 30% and then decreases by 20%. What single percentage change is equivalent to both changes? (2 marks)
16. A population of 20,000 grows at 2% per year for 3 years, then falls by 5% per year for 2 years. Find the population to the nearest whole number. (3 marks)
17. A share price rises by 40% in year 1, falls by 25% in year 2, and then rises by 10% in year 3. What is the overall percentage change from the start? (3 marks)
18. A scientist records a bacterial population of 500. It doubles (100% increase) every 6 hours. How many complete 6-hour periods does it take for the population to exceed 10,000? (2 marks)
19. An amount is increased by 25% and the result is then increased by 25%. What single percentage increase is equivalent to these two successive increases? (2 marks)
Section D: Multi-step problem solving
20. A worker earns £34,000. She receives a 5% pay rise in year 1 and a 3% pay rise in year 2. A colleague earns £36,000 and receives a 1% pay rise each year. After two years, who earns more and by how much? Give your answer to the nearest penny. (4 marks)
21. A car is bought for £22,000. It depreciates at 20% in year 1 and 12% per year in subsequent years. Find its value after 4 years to the nearest penny. (4 marks)
22. In 2020, House A cost £200,000 and rose in value by 6% per year. House B cost £260,000 and fell in value by 3% per year. In which year does House A's value first exceed House B's value? Show your working. (4 marks)
23. £P is invested at 4% compound interest per year. After 3 years the total interest earned is £2,496.12. Find P to the nearest penny. (4 marks)
24. A price is increased by 20%, and then reduced by 15%. A student claims this is equivalent to a 5% increase. Show clearly whether the student is correct. (3 marks)
25. A bank offers two savings accounts. Account A pays 3.5% compound interest per year. Account B pays 4% simple interest per year. £10,000 is invested for 6 years. Which account gives more money at the end, and by how much? Give your answer to the nearest penny. (4 marks)
Free to print and use in your classroom. No sign-up required. percentages.co.uk