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The phrase "will have cost" is grammatically correct and commonly used in written English.
It is used to talk about an action or event that will be completed at a specific point in the future. For example: "By the end of the project, it will have cost us thousands of dollars." In this sentence, we are talking about the total cost of the project at the end, which is a point in the future. Another example: "I will have finished my degree by next year." Here, we are discussing the completion of the degree in the future (next year). In summary, we can use "will have cost" to talk about a future action or event that will be completed or achieved at a specific point in time.
Exact(60)
Thus the Carnegie will have cost the city nothing.
By then, the extortion will have cost the government around $1 billion.
As of tonight, the strike will have cost nearly $5 million.
I estimate my travel will have cost me £1,000 by the end of the year.
"This project will have cost us something like a million pounds all in.
It will have cost £200m of construction to get this far.
It will have cost him time but should pay dividends in maintaining team spirit.
When completed, it will have cost about $270 million, $175 million of which has been spent.
By April 2028, it will have cost taxpayers near to £90m.
Two franchise tags already will have cost Washington nearly $44 million.
When it is completed in 2011, it will have cost nearly $100 billion.
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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