I am planning to paying off my relative's loan with interest in bank with zakat money.
Question: Is it permissible to pay off loan with interest using zakat money?
There's many opinions on this topic, so it's not possible to give a definite answer without knowing the relevant school of thought, the relationship between you and your relative, and whether or not they are Islamically "poor".
Using zakat to pay off other's debts is legitimate:
Zakah expenditures are only for the poor and for the needy and for those employed to collect [zakah] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler - an obligation [imposed] by Allah . And Allah is Knowing and Wise.
But there's conditions, and they vary with all sorts of details. For example, for Hanafi fiqh, we have:
It is permissible to give one’s Zakat to anyone who does not possess the zakatable-minimum (nisab), namely someone legally considered “poor”, as long as they are not one’s spouse, parents, or children.
SeekersHub has an Zakat Calculator which currently lists nisab as $US 4042.67.
IslamWeb writes: Whenever the expenditure is not the father's duty, like when the daughter is married, he may give Zakah to her..., which is an exception to the SeekersHub fatwa. (In fact, IslamWeb currently lists 83 fatawa on the topic.)
For Shafi'i fiqh, we have other conditions:
Each category of recipients must receive an equal share, one-eighth of the total ...
The Reliance of the Traveller, by Ahmad ibn Naqib al-Misri, translated by Nuh Ha Mim Keller
And I'm sure there's more fiqh-specific conditions I haven't listed.