How to Calculate a Discounted Price

Calculates the discounted price from the original price and the discount rate (%) as original price × (1 − rate/100).

Explanation

This takes a percentage off a price and shows both what you pay and what you save. Multiply the original price by one minus the discount rate.

y = x \left( 1 - \dfrac{r}{100} \right)

$x$ is the original price, $r$ is the discount rate in per cent and $y$ is what you pay. The saving itself is $x \times \dfrac{r}{100}$ .

Example

With an original price of 2000 and a rate of 20, $y = 2000 \times 0.8 = 1600$ , and the discount is $2000 \times 0.2 = 400$ .

Notes

"20% off" and "20% of" are opposites. Twenty per cent off means you pay 80% of the price, or 1600. Twenty per cent of the price would be just 400.

Stacked discounts do not add up. Twenty per cent off followed by a further ten per cent gives $2000 \times 0.8 \times 0.9 = 1440$ , not the 1400 a straight 30% cut would give. Since $0.8 \times 0.9 = 0.72$ , the pair is worth 28% off, not 30%.

A rate of 100 makes the item free, and anything above 100 turns the price negative. If you see that, the rate was almost certainly mistyped.