Paying by installments sounds rather like paying "up front" or in advance for lessons. That normally starts alarm bells ringing around these forums and whilst it might seem like "thread creep" is probably an issue that is more important for you to resolve than your initial question.
Apart from that Genghis is quite right....it takes what it takes and that depends on you. And Whopity has given you source material for attempting to calculate the spend versus hours relationship that you're looking for. A very very very rough guide based on my limited experience as an FI is 15 trips for the first 10 hours for a good student to get towards solo standard.
Good luck.