FileSenixSuccessive Discounts: Why 50% + 20% Is Not 70% Off
When shopping during seasonal sales or big holiday events, you will often see store banners advertising "50% OFF + Extra 20% OFF." Many shoppers quickly add the numbers in their head and assume this means a total 70% discount.
However, when you get to the checkout counter, you realize the final price is higher than you expected. In reality, a "50% + 20%" discount is actually only 60% OFF!
This mathematical trick happens because the second discount is applied to the already reduced price, not the original starting tag price. Retailers use successive (or stacked) discounts because they sound like a better deal than they actually are.
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How Successive Discounts Work (Step-by-Step)
Let us break down exactly how the math works when a store offers a successive discount.
Example: $100 Item with "50% + 20% OFF"
Original Price:$100.00
Discount 1 (50% Off $100):Saves $50.00
New Reduced Price:$50.00
Discount 2 (20% Off $50):Saves $10.00
Final Price You Pay:$40.00
Total Savings: $60 (which is exactly 60% OFF!)
Notice that the second discount (20%) is calculated on the $50 reduced price, saving you only $10. If the 20% had been calculated on the original $100 price, it would have saved you $20, giving you a total of $70 (or 70% off). That is why 50% + 20% equals 60% in retail math!
The Successive Discount Formula
If you want to calculate the single equivalent discount for any two successive discounts, you can use this handy mathematical formula:
*Where A and B are the two discount percentages.
Let's Test the Formula
Using our "50% + 20%" example: A = 50, B = 20.
- Equivalent Discount = 50 + 20 − (50 × 20 ÷ 100)
- Equivalent Discount = 70 − (1000 ÷ 100)
- Equivalent Discount = 70 − 10
- Equivalent Discount = 60%
More Examples of Stacked Discounts
30% + 10% OFF
Actual discount:
37% OFF
(Not 40%)
40% + 20% OFF
Actual discount:
52% OFF
(Not 60%)
20% + 20% OFF
Actual discount:
36% OFF
(Not 40%)
The Truth About "Buy 1 Get 1 Free" (BOGO)
Another common retail trick is "Buy One Get One" offers. While they sound like amazing deals, they are just another way of expressing percentage discounts, but they force you to buy more items.
Buy 1 Get 1 Free
You pay for 1 item and get 2 items total.
Effective Discount = 50% OFF per item
Buy 2 Get 1 Free
You pay for 2 items and get 3 items total.
Effective Discount = 33.3% OFF per item
Buy 1 Get 1 at 50% Off
You pay 100% for the first item and 50% for the second. Total paid = 150% for 2 items.
Effective Discount = 25% OFF per item
If a store offers "Buy 1 Get 1 at 50% Off," you are actually only getting a 25% discount overall. Often, buying a single item with a straight 30% discount is a much better deal, and you do not have to spend extra money on a second item you may not need!
Does the Order of Discounts Matter?
Surprisingly, NO! Applying 50% off and then 20% off gives the exact same final price as applying 20% off and then 50% off. Because multiplication is commutative, the order does not change the result: Price × 0.50 × 0.80 = Price × 0.80 × 0.50 = Price × 0.40.
Three Successive Discounts
Sometimes stores offer three discounts, like "50% + 20% + 10% OFF." Do not use the two-discount formula twice! Just calculate them sequentially. For a $100 item: $100 - 50% = $50. $50 - 20% = $40. $40 - 10% = $36. The total discount is 64% off, NOT 80% off!
Frequently Asked Questions
Why is 50% + 20% off not equal to 70% off?
Because the second 20% discount is calculated on the already reduced 50% price, not the original price. This means the 20% saves you a smaller amount of money, resulting in a total 60% discount.
What is the formula for calculating two successive discounts?
You can find the single equivalent discount using the formula: A + B − (A × B ÷ 100), where A and B are the two discount percentages.
Is 'Buy 1 Get 1 Free' the same as 50% off?
Yes and no. Mathematically, the effective discount is exactly 50% per item. However, you are forced to buy two items, which means you spend more money out of pocket than if you just bought one item at 50% off.
Does applying the smaller discount first change the final price?
No. The order of successive discounts does not matter at all. 20% off then 50% off yields the exact same final price as 50% off then 20% off.
Why do retailers use successive discounts instead of a single large discount?
Marketing psychology. A sign that says '50% + 20% OFF' catches the eye and makes shoppers think they are getting 70% off. It sounds much more appealing than a sign that accurately says '60% OFF'.
Is the Filesenix Discount Calculator free?
Yes! The Filesenix Discount Calculator is 100% free with no registration required. It easily handles stacked and successive discounts.