Is zakat obligatory on money saved to pay the housing rent due two months after the zakat due date?

If a Muslim owns a nisab and a year has passed over it, zakat becomes obligatory. If new money is acquired that is not a product of the initial wealth, there are two approaches: The first is to expedite its zakat along with the first hawl (full year), and the second is to pay the zakat for each amount separately when its own hawl is completed. The more convenient approach is to pay zakat on all savings accumulated during the year when the hawl of the first nisab owned is completed. As for money saved for rent and paid every six months, zakat is not obligatory on it because a full year has not passed over it.