I would tell her that your rate is increasing effective July 15th.
Tell her that you are raising it $10.00 a week. This is equivalent to $2.00 per day or 20 cents an hour.
Then tell her that another rate increase will take effect January 1st. Rate will go up another $15.00 a week. This is equivalent to $3.00 a day or 30 cents per hour.
Then her rate will be $500 a month. Tell her that even with the rate increase, she is basically paying for 3 weeks and getting every 4th week free compared to what your current rates are.
I had to raise my rates last year. With the cost of EVERYTHING going up, all of my parents understood.
Good luck!