Find the sale price and total savings after applying any percentage discount.
A discount reduces a price by a percentage of its original value. When a $120 jacket is marked "25% off," the sale price is $120 × (1 - 0.25) = $120 × 0.75 = $90. The formula Sale Price = Original × (1 - Discount/100) captures this directly. The savings amount is simply Original × (Discount/100) = $120 × 0.25 = $30.
Understanding discount math prevents overpaying in two common scenarios: evaluating whether a sale is actually a good deal, and stacking multiple discounts correctly. A 40% off sale on an item marked up 60% from wholesale may represent minimal actual savings — retailers frequently inflate "original" prices to make discounts appear more significant.
Working backwards from a sale price is a useful skill. If you know an item is 30% off and costs $70, what was the original price? Since $70 is 70% of the original (100% - 30% = 70%), divide by 0.70: $70 / 0.70 = $100. The formula: Original = Sale Price / (1 - Discount/100).
A common mistake is trying to add 30% back to the sale price: $70 × 1.30 = $91, which is wrong. The 30% discount was taken from $100, not from $70. Adding 30% to the reduced price gives a different (higher) number than the original because you're now applying 30% to a smaller base.
When multiple discounts apply, they compound — they don't simply add. A 20% discount followed by an additional 10% discount is not 30% off total. The math: $100 × 0.80 = $80, then $80 × 0.90 = $72. Total savings: $28, which is 28% off the original — not 30%.
The general formula for stacked discounts: Final Price = Original × (1 - d1) × (1 - d2) × ... × (1 - dn), where each d is a discount rate as a decimal. Stacked discounts are always less than the sum of the individual discounts because each successive discount applies to an already-reduced price.
Retailers use several psychological techniques around discounts that are worth understanding. "Was $200, now $120" creates an anchor around the original price. Research shows consumers evaluate the deal relative to the anchor, even when the "original" price was artificially inflated or briefly offered at that price. Compare actual prices across retailers rather than relying solely on the presented discount percentage.
Loss aversion also influences discount perception: "save $30" and "30% off" communicate identical information but may feel different psychologically. The dollar amount resonates more concretely for small items; the percentage resonates more for expensive purchases where the dollar amount of savings is large.