Double Discount Calculator: final price with two discounts

This calculator determines the final price after applying two successive discounts, showing the total savings and the equivalent single discount percentage.

Double discount formula

Successive discounts do not add, they multiply:

Final_price = Original_price × (1 − d₁) × (1 − d₂)

Where d₁ and d₂ are the discounts expressed as decimals (e.g., 20% = 0.20). The equivalent single discount is: 1 − (1 − d₁) × (1 − d₂).

Example 1: two discounts at a store

Problem: Product of $200 with 30% discount and then an additional 20%.

1. First discount:
   • $200 × (1 − 0.30) = $200 × 0.70 = $140.
2. Second discount:
   • $140 × (1 − 0.20) = $140 × 0.80 = $112.
3. Equivalent discount:
   • 1 − (0.70 × 0.80) = 1 − 0.56 = 0.44 → 44%.

Answer: Final price $112, savings of $88, equivalent discount of 44%.

Example 2: sale with additional coupon

Problem: Product of $80 with 25% discount and 10% coupon.

1. Final price:
   • $80 × 0.75 × 0.90 = $54.
2. Equivalent discount:
   • 1 − (0.75 × 0.90) = 1 − 0.675 = 0.325 → 32.5%.

Answer: Final price $54, savings of $26, equivalent discount of 32.5%.

Usos comuns

• Computing the real price in sales with additional discounts.
• Comparing offers from different stores with different discount structures.
• Verifying whether a "double discount" is truly a good deal.
• Understanding why 30% + 20% is not 50% off.
• Planning strategic purchases during sales.
• Evaluating promotions with stacked coupons.

Common mistakes with successive discounts

• Adding the percentages (30% + 20% ≠ 50%).
• Applying the second discount to the original price instead of the already discounted price.
• Not verifying whether discounts are combinable.
• Ignoring taxes applied on the final price.

Dica profissional

The order of discounts does not matter mathematically: 30% then 20% gives the same result as 20% then 30%. However, in practice, some systems apply discounts in a specific order that may affect the final result due to rounding.