Finding a Percentage

Formula: % out of total = (% ÷ 100) × total

Example: 15% of 80 = 0.15 × 80 = 12

Multiplier Method

Convert back and forth between percentages and decimals.

Example: 15% = 0.15 multiplier 7% = 0.07 multiplier

Increase/Decrease

Add/subtract the amount or use an adjusted multiplier.

Formula: Increase 20%: x 1.2 Decrease 20%: x 0.8

Example: £60 decrease 10%: 60 × 0.9 = £54

Percentage Change

Formula: (Change / Original) × 100

Example: Bought for £8, sold for £10: (2 / 8) × 100 = 25% profit

Reverse Percentages

Find original amount BEFORE a change happened.

Formula: Original = Result ÷ Multiplier

Example: After 20% increase, price is £72. 72 ÷ 1.2 = £60

Compound Interest

Interest is added each year, and the next year's interest is calculated on the NEW total.

Formula: Final = P × (Multiplier)ⁿ

Example: £1000 at 3% for 5 years: 1000 × 1.03⁵ = £1159.27

Depreciation

Value decreases by a percentage each year.

Example: Car £20k loses 15% yearly. Value after 3 years: 20000 × 0.85³ = £12,282.50

Repeated Changes

Keep multiplying by each specific change multiplier in sequence.