Is Zakat obligatory on an amount saved to pay a second installment for the price of a house, purchased through a rent-to-own agreement, knowing that paying Zakat would prevent the required amount from being paid, and that the housing program is interest-free?

Zakat (definition) is not obligatory on money saved to pay for housing installments, unless the saver has other assets (such as houses, cars, or furniture) that exceed his needs and are sufficient to cover the housing installments, and this money has reached the nisab (definition) and a full hawl (lunar year) has passed over it.