Calculate percentage increase and decrease, find the percentage change between two values, solve reverse percentage problems, and apply repeated percentage change including compound interest using multipliers.

What this dot point is asking

OCR references R9 and R16 cover percentage change and interest: percentage increase and decrease, the percentage change between two values, reverse percentages, and repeated percentage change including compound interest. The unifying tool is the multiplier, a single decimal that performs a percentage change in one step. This content appears on every tier and the calculator paper especially, and reverse percentages and compound interest are reliably high-value, frequently misanswered questions.

Percentage increase and decrease with multipliers

The multiplier method does any percentage change in one multiplication.

So increasing £$250$ by $12\%$ gives $250 \times 1.12 =$ £$280$, and decreasing $40$ kg by $35\%$ gives $40 \times 0.65 = 26$ kg. The multiplier is faster and less error-prone than finding the percentage and then adding or subtracting, and it is essential for the repeated changes that follow.

Percentage change between two values

A "find the percentage change" question compares a new value with the original.

If a share bought for £$40$ is sold for £$46$, the change is £$6$, so the percentage profit is $\dfrac{6}{40} \times 100 = 15\%$. Dividing by the wrong value (the new price) is the classic mistake, so always anchor the calculation to the original.

Reverse percentages

A reverse percentage works backwards from the value after a change.

The decisive idea is that the final amount is not $100\%$; it is $100\%$ plus or minus the change. Dividing by the multiplier recovers the original. Taking the percentage of the final amount and adjusting it is wrong because the percentage was applied to the original, not the final, value.

Compound interest and repeated change

Compound interest applies the same multiplier every period.

So £$5000$ at $4\%$ for $3$ years becomes $5000 \times 1.04^3 = 5000 \times 1.124864 =$ £$5624.32$. Compound interest differs from simple interest, where the same fixed amount is added each year; compound interest grows because each year's interest itself earns interest. The compound interest formula is given on the OCR Higher formulae sheet, but you must know how to set up the multiplier and the power.

Why this matters

Percentages model prices, taxes, savings, depreciation and population change, so OCR sets these questions in authentic financial contexts that test AO3. The multiplier is the single most useful technique, turning awkward chains of increases and decreases into one calculation, and reverse percentages are exactly the skill needed to "work back" to an original price, a common real-world task.