I’ve been freelancing for about a year now, but I’ve always charged clients a flat fee for making 100% of a site. I’ve been asked to just make a slider for the homepage with pictures and text, etc. Pretty straightforward. They want to “test me out” before I’m involved with more websites with them, but they won’t tell me their budget or how much their other developers are paid for the same work. I usually charge people on the low end for sites because I’m still new and my client’s needs are usually simple.
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If you have the outlook of more work for them, and it it is not too much work for you, I would charge them a symbolic amount 1$/€/whatever currency you get paid in and then mention it on a side note.
It will make a good impression, since veryone will know, the amount is merrely symbolic. It is far better then charging too much or too less for being tested.