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Mathematics and Statistics · Ch 9 — Commission, Brokerage and Discount

Commission and Brokerage

1

Commission and Brokerage

Much of trade is not carried on by the owner of the goods directly but through middlemen who bring buyers and sellers together and are paid for the service. This chapter studies how such payment is calculated, and how the sums due on credit transactions and on bills of exchange are worked out. These are the same commercial-arithmetic ideas set out in the standard national mathematics-and-statistics curriculum that the Maharashtra Std XII (HSC) commerce course draws upon.

An agent is a person appointed to buy or sell goods on behalf of another person, the principal. The agent does not own the goods; he only transacts in the principal's name and is paid for the service by a commission. A factor is an agent who is given possession of the goods and sells them in his own name. A broker is a middleman who merely negotiates a deal between two parties (a buyer and a seller) without handling the goods, and is paid a brokerage.

Note

Commission and Brokerage

Commission (or brokerage) is almost always a percentage of the value of the transaction — the total sales (called the turnover) an agent puts through, or the value of the deal a broker arranges.

Commission=r100×(turnover),Brokerage=r100×(value of transaction)\text{Commission} = \frac{r}{100}\times(\text{turnover}), \qquad \text{Brokerage} = \frac{r}{100}\times(\text{value of transaction})

where r%r\% is the agreed rate.

The two quantities are computed in exactly the same way; only the name of the middleman differs. When the rate is unknown it is recovered by reversing the formula, r=commissionturnover×100r = \dfrac{\text{commission}}{\text{turnover}}\times 100. A broker who acts for both the buyer and the seller earns brokerage from each side, so his total earning is the brokerage from one side taken twice.

Definition 1Agent

A person who buys or sells goods on behalf of another (the principal) and is paid a commission for the service; the agent does not own the goods.

Definition 2Principal

The owner of the goods who appoints an agent to transact on his behalf.

Definition 3Broker

A middleman who negotiates a transaction between a buyer and a seller without handling the goods, and is paid a brokerage.

Definition 4Turnover

The total value of the sales (or purchases) an agent puts through; commission is charged as a percentage of the turnover.

Definition 5Commission

Commission=r100×turnover\text{Commission}=\dfrac{r}{100}\times\text{turnover}, the payment to an agent at rate r%r\% of the value transacted.