Charging by keyword is an old tactic which can backfire since there is no guarantee how much time it will take to bring up a link on the first page. Getting new resources and pages on Google's first page has become highly complex.
I run a marketing agency and we have a lot of SEO projects running. We charge all our clients on the basis of work done on a monthly basis. If you will do good SEO work for a couple of months, the results will start trickling in in the form traffic and engagement. Use these improvements to prove your work.
You have built a site but what are you doing to get clients? Initial clients are the hardest to acquire. Case studies can be a huge asset when you are reaching out to potential clients. Look at some of our case studies to learn how to build some for yourself!
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Good luck with your work!