Here is a typical growth path for a well-developed chess kid:
- begin to learn chess in K-2
- start to play in scholastic tournaments after 6 months
- get above 1000 in two years
- reach 1500 when s/he leaves elementary school
- with some hard work, move up 100-200 a year during middle-school years, of course there are ups and downs
- before or right after s/he gets into high school, s/he should be able to reach 2000
So overall it takes about 6 to 8 years, as long as s/he persists and does the hard work. This applies to all above-average students. But not all above-average kids can persists for 6 to 8 years, especially during his/her down time. It's definitely a long term effort and commitment, but the goal is reachable for all students who can perform well in school.
A few kids may start earlier and make faster progress, such as Carissa Yip, who is the youngest (age 11) female master in US, and Hikaru Nakamura became master at age 10.