Is zakat obligatory on an apartment that was purchased in installments, half its price has been paid, and it is now intended for sale, and what is the amount of this zakat if it is obligatory?

So long as you bought the apartment for personal use and not for trade, there is no zakat due on its value, even if you intend to sell it later. If you do sell it, begin a new lunar year (hawl) count from the date of sale, and after the hawl has passed, pay a quarter of a tenth (2.5%) of its price as zakat.