"I have already put away some savings."

I'm a student in China and I read this in my textbook.

The whole sentence is:

I have already put away some savings since I made a budget.

In my opinion, you can only "put away a hundred dollars" or "put away some money" and the money you put away will turn into your savings. Thus I think there's a mistake in my textbook. But since I'm not a native speaker, I want to know whether native speakers will use this phrase.

Solution 1:

Native speakers would definitely use this phrase. "Savings" refers to the money put away, and it can be identified as "savings" even before it reaches the savings account.

From a google books search, a random example is:

And often, plans to put-away savings sooner are pushed back or delayed.

Reference: The future of social security for this generation and the next: Current state of public opinion on the future of social security