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To be taken seriously as a freelance graphic artist, you need to charge for the time you spend working on client projects. Whether you charge by the project or by the hour, your rate should reflect the cost of your time, including the equipment you need to do your work.
The Graphic Artists Guild publishes a handbook on pricing and ethical issues which may be of use in setting up your rates. You probably will also want to be aware of what your competitors are charging. You probably won't succeed by competing on price alone -- that will only attract bottom-feeder clients. Instead, develop your sales skills to position yourself as uniquely suited to solve the client's problems through great design.
At the same time, you'll want to develop a clear notion of how long it takes you to complete a given project or part of a project. You'll also want to develop a reliable system for tracking your work hours, so you can do a better job of estimating projects in the future.