The arithmetic of a sale
sale price = original × (1 − rate) · stacked = original × (1 − r₁) × (1 − r₂)
Single discounts are straightforward; everything interesting happens when offers combine. The stacked formula explains the standard retail patterns:
| Advertised | Feels like | Actually is |
|---|---|---|
| 50% + extra 20% | 70% off | 60% off |
| 40% + extra 30% | 70% off | 58% off |
| 30% + extra 10% + extra 10% | 50% off | 43.3% off |
The gap between "feels like" and "is" grows with the sizes of the discounts, at 50%+20% it is a full tenth of the original price. The calculator's effective-discount line is that gap made visible.
Sale-season tactics that survive arithmetic
- Anchor prices inflate before events. A "60% off" against a raised MRP can cost more than last month's everyday price. The only defence is knowing the real prior price, price-tracking history, not the tag.
- Convert coupons to rupees. A choice between "15% off" and "₹300 off" is a one-division problem (they cross at ₹2,000), yet most shoppers guess.
- Cashback is a discount with homework, future money, often capped, sometimes forfeited. Compare its realistic value, not its headline, against a plain discount.
- "Up to X%" means the doorway item. The stack you actually buy computes from the rates on your item, this page, not the banner.
The same math elsewhere
Stacking percentages of shifting bases is the trap behind several money mistakes: removing GST by subtraction, expecting a 10% loss to undo a 10% gain (see the percentage calculator's change mode), and misreading investment drawdowns, a 50% fall needs a 100% rise to recover, which the CAGR calculator expresses over time. Percentages are honest; bases are shifty.