What is the ruling of Islamic law regarding vowing to sponsor an orphan with a specific amount, then it becomes clear that the actual cost of sponsorship is much higher than the expected amount?

A vow contingent upon a disliked condition is disfavored. Complete orphan sponsorship entails caring for their religious and worldly affairs and their upbringing. In matters of vows, one refers to the vower's intention. If you vowed to sponsor an orphan with a specific amount (20 to 30 dinars) and it becomes apparent that the cost is greater, you are only obligated to what you intended, though an increase is better and carries a greater reward.