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The phrase "any cost for" is correct and usable in written English.
It can be used when discussing expenses or fees associated with a particular action or service.
Example: "We are willing to cover any cost for the necessary repairs to the equipment."
Alternatives: "any expense for" or "any charge for".
Exact(7)
"At any cost!" For Ida Dalser, played with deep feeling and rivers of tears by Giovanna Mezzogiorno, that cost would be devastating.
A church employee who distributes election voter guides (for which her church did not incur any cost for distribution) could not be punished by the IRS.
If the president instead opts to misinterpret the chairman's testimony as a license to hold out, at any cost, for a proposal that even Republicans on Capitol Hill were slow to embrace, he will have wasted an invaluable opportunity.
This approach, which attaches little importance to the UN, makes no attempt to understand the reluctance and indecision of its allies, and is intent on having the cooperation of local national armies at any cost for the sake of its own military victory, is not much different from that of Saddam, who recognises nothing but his own will.
With digital goods, you can give away 90% of your product for free, without any cost for those goods.
However, in our experiment, we found no evidence for any cost for the former.
Similar(53)
The city will pick up the estimated $80 million cost, as well as any costs for acquiring land.
GNM accepts no responsibility for any costs (for example travel or accommodation costs) associated with the prizes that are not expressly included in the prizes.
Or one sibling assumes, without ever discussing it with the others, that the children will split any costs for care equally.
Those costs include emergency welfare payments to parents living on benefits; bus and transport costs to ship students to different schools; staffing costs incurred from managing the crisis; and any costs for hiring additional facilities while the schools are closed.
Many subprime lenders tell borrowers they will not have to pay any fees, or even any costs for services like appraisals, but include those fees in what is called a "yield-spread premium" on the interest rate.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com