Hard Percentage Worksheet
Free to print and use in your classroom. No sign-up required.
Hard Percentage Worksheet
Key formulae
Compound interest / growth: A = P(1 + r/100)^n
Depreciation / decay: A = P(1 − r/100)^n
Reverse percentage: Original = Final value ÷ multiplier
P = starting value, r = rate (%), n = number of years, A = final amount
These questions cover all percentage topics including reverse percentages, compound interest, and percentage change. Show full working for each question.
Section A: Percentage increase and decrease with multipliers
1. Increase £340 by 15%. What multiplier do you use? What is the result?
2. Decrease 860 by 35%. Write down the multiplier and calculate the result.
3. A salary of £28,000 increases by 4.5%. Find the new salary.
4. A price of £76 is reduced by 12.5%. Find the new price.
5. A value is increased by 20% and then decreased by 20%. What is the overall percentage change? Use a starting value of £100 to show your working.
6. A shop increases its prices by 8% in January, then reduces them by 5% in June. What is the overall percentage change to 2 decimal places?
7. The value of a house increases from £180,000 to £216,000. Calculate the percentage increase.
Section B: Reverse percentages
8. After a 20% increase, a price is £660. Find the original price.
9. After a 15% reduction, a price is £272. Find the original price.
10. An item costs £94 after VAT at 17.5% is added. Find the pre-VAT price.
11. After a 6% pay rise, a worker earns £37,100 per year. What was the original salary?
12. A coat is sold for £112.50 after a 25% discount. What was the original price?
13. After two successive increases of 10%, a value is £6,050. Find the original value.
Section C: Compound interest and depreciation
14. £2,500 is invested at 4% compound interest per year for 3 years. Find the total amount to the nearest penny.
15. A car worth £16,000 depreciates at 18% per year. Find its value after 2 years to the nearest penny.
16. £800 is invested at 5.5% compound interest per year for 4 years. Find the total amount to the nearest penny.
17. A machine worth £30,000 depreciates at 12% per year for 3 years. Find its value to the nearest penny.
18. Compare: £6,000 at 3% simple interest for 4 years versus £6,000 at 3% compound interest for 4 years. What is the difference to the nearest penny?
19. A house is worth £220,000 and increases in value at 2.5% per year compound. Find its value after 5 years to the nearest pound.
Section D: Mixed word problems
20. A television costs £480. It is reduced by 15% in a sale. A customer then uses a voucher for a further 10% off the sale price. How much does the customer pay?
21. A worker earns £32,000 per year. They receive a 3% pay rise, then a further 2% rise the following year. What is their salary after both rises?
22. In 2022, a town had a population of 45,000. The population fell by 4% in 2023 and then increased by 6% in 2024. What was the population at the end of 2024, to the nearest whole number?
23. A bank account has £5,200 after interest is added at 4% per year compound for 2 years. How much was originally invested? Give your answer to the nearest penny.
24. A laptop costs £960 including VAT at 20%. An electrician can reclaim the VAT. How much does the electrician effectively pay?
25. A share is worth £3.60. It rises by 25% in March and then falls by 20% in April. What is the final value of the share? Has it returned to its original value? Explain why or why not.
Free to print and use in your classroom. No sign-up required. percentages.co.uk