Percentage Multipliers –

Percentage multipliers give you a fast, one-step way to calculate percentage increases and decreases. Instead of finding the percentage and then adding or subtracting, you multiply by a single decimal — saving time and reducing errors on both calculator and non-calculator GCSE papers.

What Are Percentage Multipliers?

A percentage multiplier is a decimal number that you multiply an amount by to apply a percentage change in a single step. For a percentage increase, the multiplier is greater than 1. For a percentage decrease, the multiplier is less than 1.

For example, to increase a value by 15%, you multiply by 1.15 (since 100% + 15% = 115% = 1.15). To decrease by 15%, you multiply by 0.85 (since 100% − 15% = 85% = 0.85).

Multipliers become especially powerful for repeated percentage change. If a value increases by 5% each year for 3 years, you multiply by 1.05 three times — or equivalently, by 1.05³. This connects directly to compound interest and depreciation.

Key Formulas

Step-by-Step Method

1. Decide whether the change is an increase or a decrease.
2. Convert the percentage to a decimal by dividing by 100.
3. For an increase, add the decimal to 1. For a decrease, subtract it from 1.
4. Multiply the original amount by the multiplier.
5. For repeated changes, raise the multiplier to the power of the number of times the change occurs, then multiply.

Worked Example 1 — Foundation Level

Question: Increase £350 by 12%.

Working:

Step 1 — This is an increase, so the multiplier = 1 + 0.12 = 1.12.

Step 2 — New amount = 350 × 1.12 = 392.

Answer: £392

Worked Example 2 — Higher Level

Question: A car worth £18,000 depreciates by 15% per year. Find its value after 3 years. Give your answer to the nearest penny.

Working:

Step 1 — This is a decrease, so the multiplier = 1 − 0.15 = 0.85.

Step 2 — The depreciation happens 3 times, so raise the multiplier to the power of 3.

Step 3 — Value after 3 years = 18,000 × 0.85³ = 18,000 × 0.614125 = 11,054.25.

Answer: £11,054.25

Worked Example 3 — Exam Style

Question: A savings account pays 3.5% compound interest per year. £2,000 is deposited. Work out the total value after 4 years. (3 marks)

Working:

Step 1 — Multiplier = 1 + 0.035 = 1.035.

Step 2 — Value = 2,000 × 1.035⁴.

Step 3 — 1.035⁴ = 1.14752... so value = 2,000 × 1.14752... = 2,295.05 (to the nearest penny).

Answer: £2,295.05

Common Mistakes

• Using 0.15 instead of 1.15 for a 15% increase. Multiplying by 0.15 gives you 15% of the amount, not the amount increased by 15%. The multiplier must include the original 100%.
• Applying repeated percentage change as a single large percentage. A 10% increase for 3 years is not a 30% increase. You must multiply by 1.10 three times, which gives 1.331 — a 33.1% increase.
• Mixing up increase and decrease multipliers. A 20% decrease uses 0.80, not 1.20. Always check: is the multiplier making the number bigger or smaller?

Exam Tips

• Write down the multiplier explicitly — examiners award a method mark for stating it correctly.
• For repeated change problems, write the expression in full (e.g. 18000 × 0.85³) before calculating. This earns method marks even if you make an arithmetic error.
• If a question asks you to find the original value before a percentage change, divide by the multiplier — this links to reverse percentages.

Practice Questions

Q1 (Foundation): Decrease £480 by 25%.

Q2 (Foundation): A TV costs £560. The price is increased by 8%. What is the new price?

Q3 (Higher): A painting increases in value by 6% each year. It is currently worth £1,200. What will it be worth in 5 years? Give your answer to the nearest pound.

Practise percentage multiplier questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Percentages
• Compound Interest and Depreciation
• Reverse Percentages

Summary

• A percentage multiplier lets you apply a percentage change in one step.
• For an increase of p%, multiply by (1 + p/100). For a decrease, multiply by (1 − p/100).
• For repeated percentage changes, raise the multiplier to the power of the number of repetitions.
• Multiplying by 0.p gives p% of the amount — not the amount after a p% change.
• Always state your multiplier clearly in exams to earn method marks.