Successive Discounts: Why 10% + 10% Isn’t 20%

The math that tricks you

A store advertises “10% off + an extra 10% in the app.” Many people add the discounts and expect 20% off. But the second discount applies to the already reduced price:

1. $100.00 with a 10% discount = $90.00.
2. $90.00 with another 10% discount = $81.00.
3. Total discount: 19%, not 20%.

The general formula for discounts d₁, d₂, … is: total discount = 1 − (1 − d1) × (1 − d2) × …. The order doesn’t matter: 10% followed by 20% gives the same result as 20% followed by 10%.

Combined discount chart

The discount calculator works out stacked discounts and shows the final price. The percentage calculator handles percentage changes and questions like “X is what percent of Y?”

Successive increases and decreases

The same logic applies to increases and decreases in prices, salaries, or investments:

• Up 50%, then down 50%: 100 × 1.5 × 0.5 = 75. You end up with 25% less, not back where you started.
• Up 10%, then down 10%: 100 × 1.1 × 0.9 = 99. That’s a 1% loss.
• Down 20%—how much does it need to go up to recover? 1 ÷ 0.8 = 1.25: it needs to go up 25%.
• Down 50%? It needs to double (go up 100%) to recover.

It’s the same principle behind compound interest and cumulative inflation: successive percentage changes are multiplied, not added.

Worked examples

1. A $250 item with 15% off in-store and a 5% coupon: 250 × 0.85 × 0.95 = $201.88. That’s a total discount of 19.25%, not 20%.
2. A salary goes up 5% one year and 6% the next: 1.05 × 1.06 = 1.113, or a cumulative increase of 11.3%, not 11%.
3. The price drops from $80 to $60: That’s a 25% decrease (20 ÷ 80). To get back to $80, it needs to increase by 33.33% (20 ÷ 60), because the starting point is now lower.
4. 10% off, followed by a 10% increase: 100 × 0.9 × 1.1 = 99. The final price is 1% below the original.

Quick rule: convert each change into a factor (15% off becomes 0.85; a 6% increase becomes 1.06), multiply them all, then compare the result with 1. Below 1 means a decrease; above 1 means an increase.

Tiered discounts and quantity deals

Deals like “buy 3, pay for 2” are equivalent to a 33.33% discount per item (you pay for 2 out of 3), but only if you’ll actually use all three. “50% off the second item” gives you a 25% discount on the two items combined: you pay 1.5 times the price of one item instead of 2 times.

For tiered discounts (10% off when you buy 2 items, 20% off when you buy 3), calculate the per-item price for each option and compare it with what you actually need. A discount on something you weren’t going to buy isn’t savings.

Black Friday: half off the doubled price

The classic trick: an item used to cost $100, the store raises the price to $200 weeks beforehand, then advertises “50% off.” The final price is back to $100—a real discount of zero.

How to protect yourself:

• Write down or take a photo of the prices of the items you want weeks before the sale.
• Use the real discount tab in the discount calculator with the price you saw before the sale, not the “was” price in the ad.
• Be wary of discounts based on prices the item was never actually sold for.

Advertising a fake discount is deceptive advertising, and consumer protection laws in most countries prohibit it. If you spot this practice, keep screenshots and receipts and report it to your local consumer protection agency. Before you buy, it’s also worth comparing paying in installments or paying upfront.

Updated October 2026.

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