If a price goes up 20% before a sale and then gets 20% off, is it back to the old price?
No, it ends up lower. A 100 product becomes 120 after the rise, and 20% of 120 is 24, so the price becomes 96. The discount is taken from the higher price, so its amount is bigger than the rise. The discount that lands exactly back on 100 is about 16.67%.
Same rate, different base
The 20% rise was taken from 100, so it added 20. The 20% discount is taken from 120, so it removes 24. The rates match, but the numbers they apply to do not, so one does not cancel the other. In one line: 1.20 × 0.80 = 0.96, which leaves you at 96% of the original.
Original price 100, after a 20% rise it is 120.
In the Discount calculator: price 120 with 20% off gives 96, a saving of 24.
Price 120 with 16.6667% off gives about 100, the original price.
Finding the discount that undoes a rise
Divide the amount of the rise by the price after the rise. A rise of 20 on a price now at 120: 20 ÷ 120 = 16.67%. A 25% rise needs a 20% discount to undo it, because 100 becomes 125, and 25 ÷ 125 = 20%.
Price 125 with 20% off gives exactly 100.
That is why some sellers lift a price 25% and then advertise 20% off: the result is the old price, with a sale sign on it.
Why this trick is a bad idea
- Regular customers remember prices, and some comparison sites and browser extensions show price history, so a 'discount' that saves nothing is easy to spot.
- Lost trust costs more than whatever one campaign earns, especially for a store that lives on repeat buyers.
- Consumer protection bodies look at prices raised just before a sale, so check the rules that apply to your store before any campaign.
Where the same maths is legitimately useful
The idea helps in honest situations too. If a supplier raised your cost and you lifted your price 20%, then want a promotion that temporarily brings customers back to the old price, the right discount is 16.67%, not 20%. At 20% you would sell below your old price, so check the profit in the Profit margin calculator before announcing it.
And for the shopper: if a product's price went up recently and then came down by the same percentage, you are paying a little less than the old price, not a lot less.
Common questions
Does it change if the discount comes first and the rise second?
No. 100 with 20% off is 80, and a 20% rise on that is 96 as well, because multiplication does not care about order.
Does the calculator work out the rise too?
No, it handles discounts only. Work out the raised price by hand, then enter it with the discount rate.