Percentages — percentage change, reverse and compound interest

Percentage change

Percentage increase/decrease = (change ÷ original) × 100.

Example: A price rises from £48 to £60. Change = 60 − 48 = 12. Percentage increase = (12 ÷ 48) × 100 = 25%.

Using a multiplier (more efficient):

• Increase of 30%: multiply by 1.30.
• Decrease of 15%: multiply by 0.85.
• Combined: original × multiplier → new value.

Example: A £250 jacket is reduced by 20% in a sale. Find the sale price. Sale price = 250 × 0.80 = £200.

Reverse percentages

When you know the amount AFTER a percentage change and need to find the ORIGINAL, use reverse percentages (work backwards from the multiplier).

Example: After a 30% increase, a salary is £26,000. What was the original salary? The multiplier for +30% is 1.30. Original = 26,000 ÷ 1.30 = £20,000.

Common mistake: students subtract 30% from £26,000 and get £18,200. This is wrong because 30% of the NEW salary, not the original.

Compound interest

Compound interest is calculated on the accumulated balance (including previously earned interest), not just the original amount.

Formula: A = P × (1 + r/100)ⁿ

Where A = final amount, P = principal, r = rate per period (%), n = number of periods.

Example: £2,000 is invested at 4% per year compound interest for 5 years. A = 2000 × (1.04)⁵ = 2000 × 1.2166... = £2433.31 (to the nearest penny).

Simple interest (for contrast): interest is calculated on the original principal only. Simple interest = P × r × n / 100.

Repeated percentage change

The compound interest formula also applies to population growth, depreciation, and inflation:

Depreciation: A car worth £12,000 depreciates by 15% per year. Value after 4 years: V = 12,000 × (0.85)⁴ = 12,000 × 0.5220... ≈ £6,264.

Combined percentage changes: an 8% increase followed by a 5% decrease. Overall multiplier = 1.08 × 0.95 = 1.026 → 2.6% overall increase (not 3%).

CCEA examiner style

CCEA Paper 2 frequently presents percentage problems in context (shop discounts, salary changes, population growth, VAT). Identify the correct base before calculating.