   SEARCH HOME Math Central Quandaries & Queries  Question from Nadja: Hi 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 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,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.