Many graphic designers eventually move away from pure hourly billing toward flat project rates once they can estimate their own speed accurately, a logo package might be quoted as a flat $800–3,000 rather than hours times a rate. If you're pricing a project flat, it's still worth dividing the flat fee by your expected hours to sanity-check it against the $15–50/hr range above, so you're not accidentally working for $8/hr on a project that ran long.
A rate only matters if it actually gets collected. Once you've picked a number, send a professional invoice that states your terms clearly, and consider a simple contract for anything beyond a quick one-off, it's the easiest way to avoid scope creep eating into that hourly number. If you want to see how your rate translates into real take-home pay after taxes and time off, try the freelance take-home pay calculator.