Discount and mark-up

Discounts and mark-ups are the two most common commercial cases of percentage decrease and increase. In both, the starting price is multiplied by a single factor.

Definition — Discount and mark-up

A discount of $p\%$ on a price $P_0$ leads to a new price $P = P_0\Bigl(1-\frac{p}{100}\Bigr).$ A mark-up of $p\%$ is instead $P = P_0\Bigl(1+\frac{p}{100}\Bigr).$

Recognising in $\bigl(1-\frac{p}{100}\bigr)$ and $\bigl(1+\frac{p}{100}\bigr)$ the multiplicative factors seen for decreases and increases lets us chain several operations simply by multiplying the factors together.

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Topics: Percentages
Concepts: Mark-up · Discount
Methods: Discount percentage
Skills: Calculating · Using formulae