Is Zakat due on a plot of land, part of which was sold due to inability to complete construction, and when is the time for its payment?

If you bought land for construction, not for trade, then there is no zakat on its value or on the buildings erected upon it. Zakat becomes obligatory in the future on the price of the land and buildings after their sale if it reaches the nisab, and zakat is paid after one Hijri year by taking one-fortieth (2.5%) of the amount.