Percentages: Increase & Decrease –

Percentage increase and decrease questions appear on virtually every GCSE Maths paper — at both Foundation and Higher tier. From sale prices and tax calculations to compound interest and depreciation, this topic has real-world applications that examiners love to test. The key to getting these questions right every time is learning the multiplier method. This guide covers simple percentage change, the multiplier method, compound changes and percentage profit or loss, with fully worked examples and exam tips for AQA, Edexcel and OCR.

What Is Percentage Increase and Decrease?

A percentage increase makes a value larger by a given percentage. A percentage decrease makes it smaller.

The multiplier method

The fastest and most reliable approach is to use a decimal multiplier.

Percentage increase: multiply by (1 + percentage as a decimal).

Percentage decrease: multiply by (1 − percentage as a decimal).

Examples of multipliers:

Finding percentage change

To find the percentage change between an original and a new value:

A positive result means increase; a negative result means decrease.

Step-by-Step Method

Simple percentage increase or decrease

1. Convert the percentage to a decimal (divide by 100).
2. Calculate the multiplier: add to 1 for increase, subtract from 1 for decrease.
3. Multiply the original value by the multiplier.

Compound percentage change (Higher)

For repeated percentage changes over multiple periods (e.g., compound interest):

1. Find the multiplier for one period.
2. Raise it to the power of the number of periods.
3. Multiply the original value by the result.

where n is the number of periods.

Finding percentage profit or loss

1. Calculate the actual profit or loss (selling price − cost price).
2. Divide by the original cost price.
3. Multiply by 100 to convert to a percentage.

Worked Example 1 — Foundation Level

Question: A laptop costs £480. In a sale, the price is reduced by 15%. Find the sale price.

Step 1: Multiplier for 15% decrease = 1 − 0.15 = 0.85

Step 2: Sale price = £480 × 0.85 = £408

Alternative method: 15% of £480 = 0.15 × 480 = £72. Sale price = £480 − £72 = £408.

Both methods give the same answer, but the multiplier method is quicker and less prone to errors.

Worked Example 2 — Higher Level (Compound Interest)

Question: £2500 is invested in a savings account that pays 3.2% compound interest per year. How much is in the account after 4 years? Give your answer to the nearest penny.

Step 1: Multiplier for 3.2% increase = 1 + 0.032 = 1.032

Step 2: After 4 years: Final value = £2500 × (1.032)⁴

Step 3: (1.032)⁴ = 1.13408... (use a calculator for this)

Step 4: Final value = £2500 × 1.134082... = £2835.21 (to the nearest penny)

Interest earned: £2835.21 − £2500 = £335.21

Note: Simple interest would give £2500 × 0.032 × 4 = £320. Compound interest gives more because you earn interest on previous interest.

Common Mistakes

• Adding or subtracting the percentage separately. Using the multiplier method (e.g., × 0.85 for a 15% decrease) is more efficient and avoids the common error of calculating the percentage correctly but then forgetting to subtract it.
• Using the wrong multiplier direction. An increase of 20% is × 1.20, not × 0.80. A decrease of 20% is × 0.80, not × 1.20.
• Applying simple interest instead of compound interest. For compound interest, you must raise the multiplier to a power. Do not multiply the single-year interest by the number of years — that is simple interest.
• Percentage change from the wrong base. Percentage change is always calculated relative to the original value, not the new value. This is a common error in profit/loss questions.
• Rounding intermediate values. When calculating compound interest, keep full calculator accuracy until the final step.

Exam Tips

1. Learn your multipliers. Being able to instantly convert percentages to multipliers saves time. Practise until 35% increase = × 1.35 and 12% decrease = × 0.88 come naturally.
2. On AQA papers, compound interest questions often ask you to "show that" or "calculate to the nearest penny". Show the full calculation including the power.
3. For Edexcel "find the percentage change" questions, always state whether it is an increase or decrease as part of your answer — marks are awarded for this.
4. Use the multiplier for VAT calculations. VAT at 20% means the price including VAT is the original × 1.20. This is faster than finding 20% and adding it on.

Practice Questions

Question 1 (Foundation): A coat originally costs £120. It is reduced by 35% in a sale. What is the sale price?

Question 2 (Foundation/Higher): A house was bought for £180,000 and sold for £207,000. Find the percentage profit.

Question 3 (Higher): A car depreciates by 12% each year. It is currently worth £15,000. What will it be worth after 3 years?

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Related Topics

• Reverse Percentages
• Ratio Basics and Sharing
• Direct and Inverse Proportion
• Fractions, Decimals and Percentages

Summary

• Percentage increase: multiply by (1 + r/100). Example: 25% increase → × 1.25.
• Percentage decrease: multiply by (1 − r/100). Example: 25% decrease → × 0.75.
• The multiplier method is the fastest and most reliable approach for all percentage questions.
• Compound interest uses the formula: Final = Original × (multiplier)ⁿ.
• Percentage change = ((new − original) / original) × 100.
• Always calculate percentage change relative to the original value.
• Keep full calculator accuracy for intermediate steps; only round at the end.