What is the ruling on Zakat for an apartment purchased with the intention of saving money and renting it out, without the intention of selling it, and is Zakat obligatory on the rental income or on the amount paid as a down payment and installments?

If the intention to sell the apartment was not made when it was purchased, then there is no zakat (definition) on its value. Rather, zakat is due on its income (rent) if it reaches the nisab (definition) and a year has passed over it, either by itself or by what is combined with it from money, gold, silver, or trade goods. Purchasing real estate with the intention of preserving wealth does not make it a trade good subject to zakat, as zakat is only obligatory on that which is intended for profit and trade.