I think an important thing to consider is just how important the activity (in the OP's case, the voice lessons) are to the child. In other words, just how badly is she wanting to do the activity?
I totally agree. The kids do have many interest and change quite often too. Most of the time, the kids wanted to do it for fun. A few times, they think they are good at it and probably compete in that sports/music, etc.. I set a limit on 1 music and 1 sports activity for my DDs. They are somewhat talented in music but not in sports. After one try out, you know that your kid has IT or not. If they do, I would have probably encouraged them to spend 1-2 hours a day practicig it and us spending a few hundreds or even a thousand $ a month.
Probably a good thing that they are not and all we spend is $200 for music lessions and $150 for gymnastics for 2 DDs.