Note that things like "down payment" (or "downpayment" but not "down-payment") are not slang. They are simply alternative ways of saying things. You don't need to say "downpayment" in order to be understood. We understand "payment in advance" perfectly well.
I can't say for sure but I think we use "down" in that phrase because, at one time, when someone said they wanted to buy something, they were expected to produce at least some of the money to show that they were serious. It's like a deposit - you put a percentage of the money down on the table and then pay the rest later.
Cruise price £1100. Put £600 down now and pay the rest in September.
I've put a deposit down on a house.
A small downpayment will secure this car.
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