Key ideas
- A multiplier does the whole percentage change in one step: a 3% increase is × 1.03, a 15% decrease is × 0.85.
- Compound change happens again and again: multiply by the multiplier to the power of the number of years.
- Reverse percentages work backwards: find what percentage you have, find 1%, then find 100%.
Compound percentage change
Stuart invests £4 500 in a savings account.
The account pays compound interest at 2.3% per year.
Calculate the amount in the account after 3 years.(3 marks)
Find the decimal multiplier.100% + 2.3% = 102.3%= 1.023✓1
In plain EnglishAdd the rate to 100%, then divide by 100. This single number represents the increase.
Raise to the power of the number of years.4500 × 1.0233✓2
In plain EnglishThe money grows for 3 years, so the power is 3.
Multiply by the starting value.= £4 815.29✓3
In plain EnglishType it into your calculator in one go. Round to 2 decimal places — it's money.
Compound appreciation
A painting is bought for £2 400. Its value appreciates by 4.5% each year. Calculate its value after 5 years.(3 marks)
Find the decimal multiplier.100% + 4.5% = 104.5%= 1.045✓1
In plain EnglishAppreciation means the value is going up. Add the rate to 100% and divide by 100. A number above 1 always means an increase.
Raise to the power of the number of years.2400 × 1.0455✓2
In plain EnglishThe painting appreciates for 5 years, so the power is 5.
Multiply by the starting value.= £2 990.84✓3
In plain EnglishType 2400 × 1.045 xy 5 into your calculator. Round to 2 decimal places.
Compound depreciation
A new car is bought for £18 500. It depreciates in value by 22% each year. Calculate its value after 3 years.(3 marks)
Find the decimal multiplier.100% − 22% = 78%= 0.78✓1
In plain EnglishDepreciation means the value is going down. Subtract the rate from 100% and divide by 100. A number below 1 always means a decrease.
Raise to the power of the number of years.18500 × 0.783✓2
In plain EnglishThe car depreciates for 3 years, so the power is 3.
Multiply by the starting value.= £8 779.21✓3
In plain EnglishType 18500 × 0.78 xy 3 into your calculator. Round to 2 decimal places.
Reverse percentages (calculator)
A jacket is on sale. After a discount of 15%, it costs £59.50. What was the original price?(3 marks)
Work out what percentage you actually have.
| 85% | → | £59.50✓1 |
In plain EnglishA 15% discount means £59.50 represents 85% of the original price. Write this as your starting point.
Find 1%.
| 1% | → | £59.50 ÷ 85 = £0.70✓2 |
In plain EnglishDivide the value you have by the percentage it represents. This gives you 1% of the original price.
Find 100%.
| 100% | → | £0.70 × 100 = £70.00✓3 |
In plain EnglishMultiply your 1% value by 100. This gives the original price before the discount.
A salary increased by 12%. The new salary is £30 464. What was the salary before the increase?(3 marks)
Work out what percentage you actually have.
| 112% | → | £30 464✓1 |
In plain EnglishA 12% increase means the new salary is 112% of the original. Write this as your starting point.
Find 1%.
| 1% | → | £30 464 ÷ 112 = £272✓2 |
In plain EnglishDivide the value you have by the percentage it represents. This gives you 1% of the original salary.
Find 100%.
| 100% | → | £272 × 100 = £27 200✓3 |
In plain EnglishMultiply your 1% value by 100 to get back to the original salary before the increase.
Reverse percentages (non-calculator)
Non-calculator tip: The numbers are chosen so that dividing by the percentage gives a whole number or simple decimal. Look for a clean division on line 2 — if it's messy, double-check your starting percentage.
A coat is reduced by 25% in a sale. It now costs £48. What was the original price?(3 marks)
Work out what percentage you actually have.
| 75% | → | £48✓1 |
In plain EnglishA 25% reduction means the sale price is 75% of the original. Write this as your starting point.
Find 1% using a clean division.
| 1% | → | £48 ÷ 75 = £0.64✓2 |
In plain EnglishIn a non-calculator question, dividing by 75 is manageable — think of it as dividing by 25 first (÷25 = £1.92), then by 3... or just divide directly. The answer will always be a simple number.
Find 100% by multiplying by 100.
| 100% | → | £0.64 × 100 = £64.00✓3 |
In plain EnglishMultiply your 1% value by 100. Moving the decimal point two places right gives the original price.
A worker's pay increased by 20%. Their new pay is £360 per week. What was their pay before the increase?(3 marks)
Work out what percentage you actually have.
| 120% | → | £360✓1 |
In plain EnglishA 20% increase means the new pay is 120% of the original. Write this as your starting point.
Find 1% using a clean division.
| 1% | → | £360 ÷ 120 = £3✓2 |
In plain English£360 ÷ 120 = £3. This is a straightforward division — the numbers in non-calculator questions are always chosen to make this step easy.
Find 100% by multiplying by 100.
| 100% | → | £3 × 100 = £300✓3 |
In plain English£3 × 100 = £300. This is the original pay before the increase.
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Your turn
Use a calculator unless the section says non-calculator. You can type money with or without the £ sign. Stuck? Tap Need a hint?
Past paper questions
Ready for exam-style questions? These collect every SQA past paper question on percentages, with answers.
Percentages: mixed questionsEvery National 5 percentages question in one PDF, with answers. Start here.maths.scot · PDF Open ↗ (opens in a new tab) Appreciation and depreciationCompound increase and decrease questions only.maths.scot · PDF Open ↗ (opens in a new tab) Reverse percentagesWorking backwards to the original amount.maths.scot · PDF Open ↗ (opens in a new tab)