put sth down
phrasal verb with put verb uk/pʊt/ usputting | put | put
to pay part of the cost of something and promise to pay the rest later:
We will give a €30 gift card to customers who put down a deposit on a new TV.
UK (US bring sth down)
to reduce the level of sth:
Shops are being forced to put their prices down in order to attract customers.