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Mathematics and Statistics · Ch 18 — Commercial Mathematics

Discount — Trade Discount and Cash Discount

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Discount — Trade Discount and Cash Discount

Sellers advertise a list price (also called the marked price, MP, or catalogue price) and then reduce it. There are two distinct reductions, applied in a fixed order.

Trade discount and cash discount

  • Trade discount — a reduction on the list (marked) price, allowed to a buyer (often a retailer) at the time of sale. It never appears in the account books; the invoice is drawn for the reduced amount. Invoice price=List price−Trade discount=List price(1−d100).\text{Invoice price}=\text{List price}-\text{Trade discount}=\text{List price}\left(1-\frac{d}{100}\right).
  • Cash discount — a further reduction on the invoice price, allowed for prompt or early payment. Amount paid=Invoice price(1−c100).\text{Amount paid}=\text{Invoice price}\left(1-\frac{c}{100}\right).

Order matters: trade first, then cash

Note

The two discounts are successive, not additive

Trade discount is computed on the list price; cash discount is then computed on the already-reduced invoice price — not on the original list price. So a 10%10\% trade discount followed by a 5%5\% cash discount is not a flat 15%15\%:

Amount paid=List price(1−d100)(1−c100).\text{Amount paid}=\text{List price}\left(1-\frac{d}{100}\right)\left(1-\frac{c}{100}\right).

Tip

Successive discounts of a%a\% then b%b\% …

Definition 1List price (Marked price, MP)

The catalogue/tag price before any discount — the base on which trade discount …

Definition 2Trade discount

A reduction on the list price at the time of sale; the invoice is made for MP(1−d100)\text{MP}\left(1-\tfrac{d}{100}\right). It is not recorded …

Definition 3Cash discount

A further reduction on the invoice price for prompt payment; amount paid =Invoice(1−c100)=\text{Invoice}\left(1-\tfrac{c}{100}\right). Applied after, and o …