Should zakat be paid on houses designated for recreation?

Zakat (definition) is not obligatory on houses purchased for recreation, because they are considered personal assets, and there is no zakat on them according to the Prophet's (PBUH) saying: "There is no sadaqah (definition) (zakat) on a Muslim for his slave or his horse." However, if the houses are rented out for recreation and tourism, there is no zakat on the property itself. Rather, zakat becomes obligatory on the rental income if it reaches the نصاب (the equivalent of 85 grams of gold or 595 grams of silver) and a full year has passed since its acquisition, and a quarter of a tenth (2.5%) is to be paid as zakat.