Double Discount Calculator
Calculate the final price after applying two sequential discounts to an original price. Also computes total savings and the equivalent single discount rate.
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How Double Discounts Work
When two discounts are applied sequentially:
- The first discount is applied to the original price.
- The second discount is applied to the already discounted price.
Key Formula:
Final Price = Original Price × (1 - Discount1/100) × (1 - Discount2/100)
Equivalent Single Discount = 100 × (1 - (1 - Discount1/100) × (1 - Discount2/100))
Double Discount Examples
Example 1: $100 with 20% + 10% Discounts
Original Price: $100
First Discount (20%): $100 × 0.20 = $20 → New Price = $80
Second Discount (10%): $80 × 0.10 = $8 → Final Price = $72
Total Savings: $100 - $72 = $28
Equivalent Single Discount: 28% (since $72 is 72% of $100)
Example 2: $50 with 15% + 5% Discounts
Original Price: $50
First Discount (15%): $50 × 0.15 = $7.50 → New Price = $42.50
Second Discount (5%): $42.50 × 0.05 = $2.13 → Final Price = $40.38
Total Savings: $50 - $40.38 = $9.62
Equivalent Single Discount: 19.24%
Example 3: $200 with 25% + 25% Discounts
Original Price: $200
First Discount (25%): $200 × 0.25 = $50 → New Price = $150
Second Discount (25%): $150 × 0.25 = $37.50 → Final Price = $112.50
Total Savings: $200 - $112.50 = $87.50
Equivalent Single Discount: 43.75% (not 50%)
Example 4: $80 with 10% + 15% Discounts
Original Price: $80
First Discount (10%): $80 × 0.10 = $8 → New Price = $72
Second Discount (15%): $72 × 0.15 = $10.80 → Final Price = $61.20
Total Savings: $80 - $61.20 = $18.80
Equivalent Single Discount: 23.5%
Example 5: $150 with 30% + 10% Discounts
Original Price: $150
First Discount (30%): $150 × 0.30 = $45 → New Price = $105
Second Discount (10%): $105 × 0.10 = $10.50 → Final Price = $94.50
Total Savings: $150 - $94.50 = $55.50
Equivalent Single Discount: 37%
Example 6: $500 with 40% + 5% Discounts
Original Price: $500
First Discount (40%): $500 × 0.40 = $200 → New Price = $300
Second Discount (5%): $300 × 0.05 = $15 → Final Price = $285
Total Savings: $500 - $285 = $215
Equivalent Single Discount: 43%
Example 7: $75 with 50% + 20% Discounts
Original Price: $75
First Discount (50%): $75 × 0.50 = $37.50 → New Price = $37.50
Second Discount (20%): $37.50 × 0.20 = $7.50 → Final Price = $30
Total Savings: $75 - $30 = $45
Equivalent Single Discount: 60%
Example 8: $120 with 10% + 10% Discounts
Original Price: $120
First Discount (10%): $120 × 0.10 = $12 → New Price = $108
Second Discount (10%): $108 × 0.10 = $10.80 → Final Price = $97.20
Total Savings: $120 - $97.20 = $22.80
Equivalent Single Discount: 19% (not 20%)
Example 9: $99 with 5% + 5% Discounts
Original Price: $99
First Discount (5%): $99 × 0.05 = $4.95 → New Price = $94.05
Second Discount (5%): $94.05 × 0.05 = $4.70 → Final Price = $89.35
Total Savings: $99 - $89.35 = $9.65
Equivalent Single Discount: 9.75%
Example 10: $1000 with 25% + 15% Discounts
Original Price: $1000
First Discount (25%): $1000 × 0.25 = $250 → New Price = $750
Second Discount (15%): $750 × 0.15 = $112.50 → Final Price = $637.50
Total Savings: $1000 - $637.50 = $362.50
Equivalent Single Discount: 36.25%
Frequently Asked Questions
1. Why isn't the equivalent single discount just the sum of the two discounts?
Because the second discount is applied to a reduced amount. For example, 20% + 10% doesn't equal 30% because the 10% is taken from the already discounted price.
2. Does the order of discounts matter?
Mathematically, no. A 20% discount followed by 10% gives the same result as 10% followed by 20%.
3. How do I calculate the equivalent single discount rate?
Use: Equivalent Discount = 100 × (1 - (1 - D1/100) × (1 - D2/100)) where D1 and D2 are your two discounts.
4. What's the maximum possible double discount?
The theoretical maximum is 100% (free), achieved by any combination where the discounts sum to 100% (e.g., 60% + 40%).
5. Why do stores use sequential discounts instead of one larger discount?
Marketing psychology - multiple discounts may appear more significant to customers than a single larger discount.
6. How do I add a third discount?
Multiply by (1 - D3/100). Formula becomes: Original Price × (1 - D1/100) × (1 - D2/100) × (1 - D3/100).
7. Can I use this for price increases instead of discounts?
Yes, use negative percentages (e.g., -10% for a 10% price increase).
8. How does this differ from adding the percentages?
Adding percentages (20% + 10% = 30%) would give $70 in our first example, but the correct sequential calculation gives $72.
9. What's the formula for total savings?
Total Savings = Original Price - Final Price
10. Can discounts exceed 100%?
No, discounts are capped at 100% (free product). Values over 100% will be treated as 100%.
