Successive (Chain) Discounts

Sometimes a seller allows more than one discount on the same invoice, one after another — for example, a $20\%$ trade discount followed by a further $10\%$ discount for prompt cash payment. These are called successive discounts (or a discount chain), and the crucial point to understand is that each discount is applied to the price that remains after the previous discount, not to the original list price each time.

A very common mistake is to simply add the discount rates together (treating $20\%$ then $10\%$ as one $30\%$ discount) — this always overstates the true combined discount, because the second discount is computed on an already-reduced amount, not on the full list price. The genuine combined effect is captured instead by the equivalent single discount rate: