The phrase "big amount of money" is correct and usable in written English. You can use this phrase when you want to emphasize the size of a sum of money, as in the example sentence: "He won a big amount of money in the lottery.".
That's a big amount of money".
They had a quite big amount of money.
"It is a big amount of money, no matter how you slice it," Doubleday said.
We spend a big amount of money, and most people figure they don't get a good return.
"Big amounts of money bring out the characters".
Elsewhere, starving artists occupy most of the landscape, but big amounts of money float around their world.
Now, there is fear that big drug companies will be more hesitant to offer big amounts of money for the products of biotechnology companies.
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia