30% off plus 20% more: is that half price?

Take 30% off a 100,000-won jacket and it costs 70,000 won. Take another 20% off, and 20% of 70,000, or 14,000 won, comes off, leaving 56,000 won. It is not 20% of the original price, or 20,000 won.

The easy way is to multiply what remains instead of the discount rates. A 30% discount means multiplying by 0.7, and a 20% discount means multiplying by 0.8, so 0.7 × 0.8 = 0.56: you pay 56% of the original price. Applying the 20% first gives the same result.

In a 2007 paper, the American marketing researchers Chen and Rao showed in experiments that people tend to add successive percentages instead of multiplying them. A 20% discount followed by an extra 25% works out to exactly 40% off, yet many people felt it was closer to 45%.

When the two formats were compared in a real store, more people bought, and sales were higher, when the discount came in two steps, even though the price was the same. Faced with two numbers, the mind reaches for the familiar habit of adding first.

By the same logic, raising a price by 50% and then cutting it by 50% does not bring it back to where it started. 10,000 won becomes 15,000 won, then half of that, 7,500 won. That is 25% cheaper than at first.

The same holds when the news says something fell 10% and then rose 10% again. 100 becomes 90 and then 99, so it is still 1 short of where it began.

When two discounts are stacked, multiply the two remaining shares. 40% off plus an extra 10% is 0.6 × 0.9 = 0.54, which means 46% off. Use that number when comparing it with a 50% sale at the shop next door.

A coupon that takes off a fixed amount, like 5,000 won, can give a different price depending on whether it is used before or after the percentage discount. On a 100,000-won jacket, using the coupon first gives 66,500 won, and using it last gives 65,000 won. Stores differ in the order, so it is worth asking at the counter.