Math CentralQuandaries & Queries


Question from Nadja:


Our company charges a 4% margin on top of a pay rate to obtain the total charge rate. A client is denying that the total charge rate is calculated in the following way:

Pay rate/0.96 = Charge rate

Please could you provide me with an explanation which I can pass on as to why it is calculated in this way?

Many thanks

Hi Nadja,

The client's bill from you is made up of two pieces, the pay rate and a markup. If you want to express the markup as a percentage you have two choices. The first is to express the markup as a percentage of what the client pays. Thus from the client's point of view, when he sees your bill he knows that 4% of that bill is your markup. This is the margin. Hence, since 4% of the charge rate is the markup 96% of the charge rate is the pay rate. That is

0.96 × charge rate = pay rate

and thus

charge rate = pay rate /0.96.

The second option is to express the markup as a percentage of your costs. In this case you would add 4% of the pay rate to obtain the charge rate. In this case

charge rate = pay rate + 0.04 × pay rate = 1.04 × pay rate.

This method is commonly called the percentage markup.

Since you are quoting a 4% margin you are using the correct calculation.

I hope this helps,

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