From finding a simple percentage of an amount to reverse percentages and compound interest — every method explained step by step with fully worked exam questions.
A percentage is a number expressed as a fraction of 100. The word comes from the Latin per centum, meaning "out of a hundred." The symbol % represents "per hundred."
So 45% means 45 out of every 100, which as a fraction is 45/100 and as a decimal is 0.45. Being comfortable moving between these three forms — percentage, fraction, decimal — is the foundation of every percentage calculation.
To find a percentage of a quantity, convert the percentage to a decimal and multiply.
Question: Find 35% of £260.
0.35 × 260 = £91
Alternatively, use the fraction method: 35% = 35/100, so (35 × 260) ÷ 100 = 9100 ÷ 100 = £91. Both methods work; the decimal method is faster on a calculator.
For non-calculator papers, build up the answer from easy percentages you can find quickly:
Example: Find 17.5% of £80 without a calculator.
10% of £80 = £8
5% = £4
2.5% = £2
17.5% = £8 + £4 + £2 = £14
Divide the part by the whole, then multiply by 100.
Formula: Percentage = (part ÷ whole) × 100
Question: A student scores 48 out of 60. What is their percentage score?
(48 ÷ 60) × 100 = 0.8 × 100 = 80%
Make sure the part and whole are in the same unit before dividing. If you scored 450 marks out of a maximum of 600, the calculation is the same: (450 ÷ 600) × 100 = 75%.
Percentage change tells you how much a quantity has grown or shrunk compared to its original value.
Percentage change = (change ÷ original) × 100
Question: A jacket costs £80. Its price rises to £92. Find the percentage increase.
Change = £92 − £80 = £12
Percentage increase = (12 ÷ 80) × 100 = 15%
Question: A TV was £450 and is now on sale for £360. Find the percentage decrease.
Change = £450 − £360 = £90
Percentage decrease = (90 ÷ 450) × 100 = 20%
The quickest method uses a multiplier. Add the percentage to 100% for an increase, or subtract for a decrease, then convert to a decimal.
Question: A salary of £32 000 increases by 6%. Find the new salary.
£32 000 × 1.06 = £33 920
A reverse percentage problem gives you the value after a percentage change and asks you to find the original value. The most common mistake is calculating a percentage of the final value — this gives the wrong answer because percentages are always calculated on the original.
Use the multiplier approach: divide the given value by the multiplier that was applied.
Question: A coat costs £68 after a 15% reduction. What was the original price?
A 15% reduction uses multiplier 0.85. So: £68 ÷ 0.85 = £80
Check: 15% of £80 = £12; £80 − £12 = £68 ✓
Question: After a 12% pay rise, an employee earns £2 240 per month. What was their original salary?
Multiplier = 1.12. Original = £2 240 ÷ 1.12 = £2 000
Simple interest is calculated on the original (principal) amount only — it does not compound. The formula is:
Interest = (P × R × T) ÷ 100
Where P = principal, R = rate per year (%), T = time in years.
Question: Calculate the simple interest on £500 at 4% per year for 3 years.
Interest = (500 × 4 × 3) ÷ 100 = 6000 ÷ 100 = £60
Total amount = £500 + £60 = £560
Compound interest is calculated on the growing total — each year's interest is added to the principal before the next year's interest is calculated. It grows faster than simple interest over time.
Formula: A = P × (1 + r/100)n
Where A = final amount, P = principal, r = annual rate %, n = number of years.
Question: £2 000 is invested at 5% compound interest per year for 3 years. Find the total amount.
A = 2000 × (1.05)3
1.053 = 1.157625
A = 2000 × 1.157625 = £2 315.25
Compare this to simple interest: 3 years at 5% on £2 000 = £300 interest, giving £2 300 total. Compound interest earns an extra £15.25 because interest is earned on interest.
Percentages appear in every real-world context — bank accounts, exam scores, sale prices, tax, population growth. Getting every method right here pays off both in the exam and well beyond it.