The country in question is China. Using expected future fertility rates from the United Nations (which must comport with their own analysis, or they would have used their own numbers), the Chinese Academy of Social Sciences reported that:
The Chinese population will peak at 1.442 billion people a decade from now in 2029.
From 2030 on, the population base will shrink by 0.3% annually until 2050, at which point it will be 1.364 billion.
The trend to a smaller Chinese population will extend to at least 2065, at which point the country will be back to levels last seen in 1996 (1.248 billion).
All this assumes fertility rates increase from the current 1.6 children per woman to 1.77 by the end of the forecast horizon. The researchers note that if fertility rates remain constant, China's population will decrease to 1.172 billion people by 2065, the same as it was in 1990.
Link to the report at the end of this section. Google Translate works well here.