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Should a PRIVATE GUITAR TEACHER ask for money up front or after the lessons over?

I want to give private guitar lessons but i've never done it before, should i ask for money up front, or maybe only once a month?

Should i have my students sign a contract saying they'll pay me?

I give my first lesson as a free trial. When my student wants more lessons, he pays for a month, including the first lesson. When he is not content I earn nothing, but this occurs only every now and then.
I use a standard contract after a model from a consumer's league when the student insists. In my circumstances I can do without a contract but you may need one for the revenue agency.