Is it permissible for a Muslim to spend zakat money on an orphan he sponsors, such that the zakat is calculated from the predetermined monthly sponsorship amount?

If the giver of zakat has obligated himself to spend on the orphan through a vow or similar commitment, then it is not permissible for him to give zakat to the orphan. This is because by doing so, he would be reducing a portion of the expenditure that is obligatory upon him. However, if he spends on the orphan voluntarily, without any prior obligation, then there is no objection to giving zakat to this orphan, provided that the orphan is eligible to receive zakat.