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Discount calculations tell you the sale price after a percentage reduction, how much you save, and โ importantly โ how to reverse-calculate the original price from a discounted amount. The key insight is that multiple discounts must be applied sequentially (multiplicatively), not added together.
Discount Formulas
Sale price:
Original ร (1 โ Discount% รท 100)
Savings:
Original ร (Discount% รท 100)
Discount %:
(Original โ Sale) รท Original ร 100
Original price:
Sale Price รท (1 โ Discount% รท 100)
Original price: $200 | First discount: 25% off | Extra coupon: 15% off
After 25% off: $200 ร 0.75 = $150. After extra 15% off: $150 ร 0.85 = $127.50. Total savings: $72.50. Effective discount: 72.50 รท 200 = 36.25% (not 40% โ discounts stack, not add).
Sale Price = Original Price ร (1 โ Discount% รท 100). Savings = Original Price ร (Discount% รท 100). Example: 30% off $85: Sale price = $85 ร (1 โ 0.30) = $85 ร 0.70 = $59.50. Savings = $85 ร 0.30 = $25.50. Quick mental math: for 10% off, move the decimal left one place and subtract. For 20% off, double that. For 25% off, divide by 4. For 50% off, halve the price.
Original Price = Sale Price รท (1 โ Discount% รท 100). Example: an item is $63 after a 30% discount โ what was the original price? $63 รท (1 โ 0.30) = $63 รท 0.70 = $90. Common mistake: adding the discount percentage back to the sale price ($63 + 30% of $63 = $81.90 โ wrong, because 30% of the sale price โ 30% of the original price). Always divide by (1 โ discount rate) to reverse a percentage discount.
Discount% = (Original Price โ Sale Price) รท Original Price ร 100. Example: item was $120, now $84: Discount% = (120 โ 84) รท 120 ร 100 = 36 รท 120 ร 100 = 30% off. This formula tells you the true discount regardless of how the sale is labeled. Useful for comparing "buy one get one 50% off" vs "25% off both items" โ BOGO 50% = 25% off total (same math), assuming equal-priced items.
Multiple discounts are not additive โ they are multiplicative. A 20% discount followed by an additional 10% discount is not 30% off. Correct calculation: apply each discount sequentially. $100 with 20% off = $80. Then 10% off $80 = $72. Total discount = (100 โ 72) รท 100 = 28% off (not 30%). Formula: Final Price = Original ร (1 โ D1/100) ร (1 โ D2/100) ร ... Retailers use this to their advantage โ "extra 10% off already-discounted prices" sounds like more than it is.
In retail, a discount is a price reduction given to specific customers (loyalty members, employees, bulk buyers) while the listed price stays the same. A markdown is a permanent reduction in the listed (retail) price โ the tag price changes. From a calculation standpoint, the math is identical: both reduce the selling price from an original reference price. The distinction matters for accounting and inventory management: markdowns affect gross margin reporting differently than discounts.
Studies consistently show that roughly 60โ70% of "Black Friday deals" are not the lowest price of the year. Consumer research (WalletHub, NerdWallet, Adobe Analytics) found that the same or better prices are available in October, December, or January for most categories. Genuinely good Black Friday categories: TVs (major brand models are often at their best annual price), appliances, and some clothing. Use tools like CamelCamelCamel (Amazon price history), Honey, or Rakuten to verify whether a "sale price" is actually lower than the item's 90-day price history before purchasing.
Common retail pricing tactics: Anchor pricing โ showing a high "original" price next to the sale price (the original may be inflated or the item rarely sold at full price). Charm pricing โ ending prices in .99 or .97 (consumers perceive $9.99 as much less than $10 despite the $0.01 difference). Percentage vs dollar framing โ "save 20%" sounds better for expensive items; "save $20" sounds better for cheap items. Bundle pricing โ making it hard to compare individual item prices. Decoy pricing โ adding a third option that makes the middle option seem like the best value.
BOGO deals have several variations: Buy One Get One Free (BOGO 100% off): you pay for 1, get 2. Effective discount = 50% off each item. Buy One Get One 50% Off: you pay full price for first, half price for second. Effective discount = 25% off total (for equal-priced items). Buy One Get One 30% Off: 15% off total (for equal-priced items). Formula: Effective discount% = BOGO discount% รท 2. Always compare the per-item price to other deals rather than judging by the promotional framing.
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