The Discount Formula in 30 Seconds
Every discount problem uses the same three ingredients: original price, sale price, and discount rate. The discount amount equals original price times discount rate divided by 100. The sale price is simply original minus discount, or equivalently original times (1 minus discount rate over 100). A $60 coat at 25% off: discount is 60 times 0.25, which is $15, so you pay $45.
To find the discount percentage from two prices, flip it: discount percent equals (original minus sale) divided by original, times 100. That $60 coat selling for $45 gives (60 minus 45) divided by 60, which is 0.25, or 25% off. One formula, two directions, and you can verify any price tag in seconds.
Stacked Discounts: Why 20% Plus 10% Is Not 30%
Stores love stacked offers: take 20% off, plus an extra 10% off the sale price. Shoppers add them to 30%, but each discount applies to the already-reduced price. On $100: 20% off gives $80, then 10% off $80 gives $72. The real total discount is 28%, not 30%. The gap widens with bigger numbers: two 50% discounts give 75% off, not 100%.
The exact formula for two successive discounts is: equivalent discount equals d1 plus d2 minus (d1 times d2 divided by 100). For 20% and 30%: 20 + 30 minus 600/100 = 44% total, and $100 becomes $56. For three or more, just chain the multiplications: price times (1 - d1) times (1 - d2) times (1 - d3). Stacked discounts always come out lower than the sum, because each percentage bites a smaller number.
Reverse It: Finding the Original Price
Sometimes you only see the sale price and the discount percent, and want the original. The reverse formula is: original price equals sale price divided by (1 minus discount rate over 100). A laptop on sale for $850 at 15% off was originally 850 divided by 0.85, which is $1,000. A car at $11,000 after 15% off was originally 11,000 divided by 0.85, about $12,941.
This reverse calculation is also how you audit a store's claim. If the tag says was $899, now $699, run (899 minus 699) divided by 899: that is 22.2%, not the 30% the salesperson claimed. When the advertised percent and your math disagree, trust your math.
Seven Fake-Discount Tricks Retailers Use
Knowing the math is only half the battle; retailers deploy well-studied pricing psychology against it. Research on fictitious pricing shows these patterns are deliberate and widespread. The most common is the inflated was-price: the retailer raises the listed price briefly, then discounts back to the normal selling price, so the crossed-out number was never real. Endless sales are the same trick in slow motion: if something is 70% off every week of the year, that is the price, not a discount.
Other tactics include fake countdown timers that reset at zero, permanent limited stock warnings, misleading manufacturer RRPs that were never charged, loss leaders priced below cost to pull you into buying full-price items alongside, and bundle deals that cost more per item than buying separately. Your defense is always the same: check the price history online, compare the exact model across stores, and run the discount formula yourself.
- Inflated was-prices: the crossed-out price was raised just before the sale.
- Endless sales: a discount that never ends is not a discount, it is the price.
- Fake countdown timers that reset instead of expiring.
- Misleading RRPs no retailer ever actually charged.
- Loss leaders: one cheap item designed to fill the rest of your cart.
- Bundle illusions: check the per-item price before assuming savings.
Mental Math Shortcuts for the Store Aisle
You do not need a calculator for most tags. Ten percent is the price divided by 10: 10% off $80 is $8, so you pay $72. Fifteen percent is 10% plus half of 10%: on $80 that is $8 + $4 = $12 off. Twenty-five percent is the price divided by 4; fifty percent is half. Thirty percent is just three times the 10% figure.
For the common 20% off, multiply by 0.8 directly, or find 20% and subtract. And remember the tax trap: apply the discount first, then add sales tax on the reduced subtotal. A $100 item at 20% off with 8% tax is 80 times 1.08, which is $86.40, not $88. Our free Discount Calculator handles stacked discounts, tax-inclusive totals, and reverse price lookups for the cases where mental math runs out.
