Percentages and exponential change

• Find a percentage of a quantity, and express one quantity as a percentage of another.
• Calculate percentage increase and decrease, profit and loss, discount, deposit and percentages over 100%.
• Calculate simple and compound interest; the formulas are not given.
• Use reverse percentages to find an original amount, such as a cost price.
• Use exponential growth and decay, such as depreciation and population change.

Build from 10%, 5% and 1% without a calculator

Without a calculator, find 10% (÷ 10), 5% (half of 10%) and 1% (÷ 100), then combine. With a calculator, use a multiplier: 35% of 240 = 0.35 × 240. To write one quantity as a percentage of another, divide and multiply by 100, using the same units.

Change ÷ original × 100

Always divide the change by the original value. Profit or loss is an amount; as a percentage it is (profit ÷ cost price) × 100.

Learn both; neither formula is given

Simple interest is the same every year, worked out on the original amount. Compound interest is added to the amount each year, so the next year earns interest on the interest.

Divide by the multiplier

When you know the amount after a percentage change, divide by the multiplier to get back to the original. Never take the percentage of the new amount.