A United Nations document "World Population Prospects - The 2006 Revision" (PDF file) has India's total fertility rate (TFR, number of children per woman, projected, "medium variant")
2005-2010: 2.81
2010-2015: 2.54
2015-2020: 2.32
The "World Population Prospects, 2015 revision" has revised these to:
2005-2010: 2.80
2010-2015: 2.48
2015-2020: 2.34
The Indian National Family Health Survey (NFHS) has these total fertility rate figures.
NFHS-3 (2005-2006): 2.7
NFHS-4 (2015-2016): 2.2
As you can see, NFHS-3 is right in the middle of the UN figures; but NFHS-4 shows TFR has fallen faster than the medium-variant projection.
Per the 2005 UN document, India's 2050 population ("medium variant") was projected to be 1.658 billion, per the 2015 document 1.705 billion.
In the "low variant" of UN's 2015 population projection, India's TFR 2015-2020 is 2.09, and its population in 2050 is projected to be 1.509 billion.
Thus the "low variant" population projection is still a viable lower bound for India's population; the "medium variant" is an upper bound that can be tightened substantially, I think.
But we also see that projections just ten years out can be wrong, so perhaps more useful is what India's 2021 census will show. The low variant is 1.387 billion; the medium variant is 1.404 billion. The difference is about a Netherlands' worth of population.
2005-2010: 2.81
2010-2015: 2.54
2015-2020: 2.32
The "World Population Prospects, 2015 revision" has revised these to:
2005-2010: 2.80
2010-2015: 2.48
2015-2020: 2.34
The Indian National Family Health Survey (NFHS) has these total fertility rate figures.
NFHS-3 (2005-2006): 2.7
NFHS-4 (2015-2016): 2.2
As you can see, NFHS-3 is right in the middle of the UN figures; but NFHS-4 shows TFR has fallen faster than the medium-variant projection.
Per the 2005 UN document, India's 2050 population ("medium variant") was projected to be 1.658 billion, per the 2015 document 1.705 billion.
In the "low variant" of UN's 2015 population projection, India's TFR 2015-2020 is 2.09, and its population in 2050 is projected to be 1.509 billion.
Thus the "low variant" population projection is still a viable lower bound for India's population; the "medium variant" is an upper bound that can be tightened substantially, I think.
But we also see that projections just ten years out can be wrong, so perhaps more useful is what India's 2021 census will show. The low variant is 1.387 billion; the medium variant is 1.404 billion. The difference is about a Netherlands' worth of population.