How do you calculate the price after a discount?
Discounted price = Original price × (1 − discount% ÷ 100). Equivalently: Discount amount = Original price × discount% ÷ 100, then Final price = Original price − Discount amount. Example: a $80 item with 25% off: Discount = $80 × 0.25 = $20. Final price = $80 − $20 = $60. Quick mental shortcut: "25% off" means you pay 75%, so $80 × 0.75 = $60.
How do you calculate the discount percentage from two prices?
Discount% = ((Original price − Sale price) ÷ Original price) × 100. Example: item originally $120, on sale for $84: Discount% = ((120 − 84) ÷ 120) × 100 = (36 ÷ 120) × 100 = 30% off. This is useful for quickly checking whether a "sale" is actually a good deal, or for calculating implied discounts when a competitor's price is lower than yours.
How do successive discounts work — is 20% + 10% off the same as 30% off?
No — successive discounts compound, not add. A 20% discount followed by a 10% discount = 1 − (0.8 × 0.9) = 1 − 0.72 = 28% total discount — not 30%. The second discount applies to the already-reduced price. This is why retailers sometimes advertise "stacked" discounts: "an extra 10% off our already 40% off sale" sounds better than saying the total is 46% off. Always multiply the remaining percentages to find the true combined discount.
How do I calculate the original price from a discounted price?
Original price = Discounted price ÷ (1 − discount% ÷ 100). Example: you pay $63 after a 30% discount. Original = $63 ÷ (1 − 0.30) = $63 ÷ 0.70 = $90. This reverse calculation is also useful for reverse-engineering VAT: if a price includes 20% VAT and you need the pre-tax amount, divide by 1.20. A common mistake is subtracting 30% from $63 instead of dividing by 0.70.
What is the psychology behind discounting and how do retailers use it?
Retailers use several pricing psychology techniques: Anchor pricing — showing a high "original" price next to a lower sale price makes the discount feel larger (even if the original was rarely charged). Round number thresholds — $49.99 instead of $50 keeps the price in a lower perceived bracket. Loss framing — "save $30" is more motivating than "pay $70." BOGOF (Buy One Get One Free) = 50% off, but shoppers perceive BOGOF as a better deal. Understanding these tactics helps consumers evaluate whether a discount represents genuine savings.