Percentages: everyday calculations
Calculating a discount, a price increase, a % change: the everyday percentage formulas, without getting them wrong.
Calculating a percentage of a number
Result = (number × percentage) / 100
Example: 20% of 150 = (150 × 20) / 100 = 30
Applying a discount or an increase
Price after discount = original price × (1 − discount / 100) Price after increase = original price × (1 + increase / 100)
Example: a 30% discount on €80 → 80 × (1 − 0.30) = €56
Calculating a percentage change
Change (%) = ((new value − old value) / old value) × 100
A positive result means an increase, negative means a decrease.
A 50% drop followed by a 50% rise does NOT bring you back to the original price: 100 → 50 (−50%) → 75 (+50% of 50) — the starting and ending points don't share the same calculation base.
Finding the original price from a discounted price
Original price = discounted price / (1 − discount / 100)
Example: an item at €56 after a 30% discount → 56 / (1 − 0.30) = €80
Percentage points vs. percentage
Going from 20% to 25% is a rise of 5 percentage points, but a rise of 25% in relative terms ((25−20)/20 × 100). The two phrasings don't say the same thing — a common source of confusion in the news.
Simple vs. compound interest
Simple interest = principal × rate × time Balance with compound interest = principal × (1 + rate)^time
Example on €1000 at 5% per year for 10 years:
- Simple interest: 1000 × 0.05 × 10 = €500 in interest (total €1500)
- Compound interest: 1000 × (1.05)^10 ≈ €1629 (total, i.e. €629 in interest)
The gap between the two grows over time: compound interest earns interest on interest already accrued, not just on the original principal.
Calculating sales tax (gross ↔ net)
Gross price = net price × (1 + tax rate / 100) Net price = gross price / (1 + tax rate / 100) Tax amount = gross price − net price
Example at 20%: an item at €120 gross → net = 120 / 1.20 = €100, tax = €20.
Thanks for the feedback!