Saving money you already have is just as useful as earning new money.
An expression similar to our modern-day usage is found in George Herbert's Outlandish Proverbs (c.1633):
A penny spar'd is twice got.
The notion "twice got" seems to relate to the rather fuzzy math concept that by not spending a penny now and instead saving it, you are a penny up rather than a penny down, thus 'twice got'. Incidentally, back in George Herbert's day outlandish was understood in its literal sense--something that came from an outland, that is to say was foreign. Like many of his contemporaries, Herbert was a collector of aphorisms--Outlandish Proverbs includes more than a thousand aphorisms collected from across Europe.
A few decades later, in the early 1660s Thomas Fuller's The history of the worthies of England, notes that:
By the same proportion that a penny saved is a penny gained, the preserver of books is a Mate for the Compiler of them.
This is the earliest recorded use of the expression with its modern day meaning. Overtime, gained turned to got, and eventually got became earned. The earliest known usage in its present-day form is in an 1899 edition of Pall Mall Magazine--a British monthly literary magazine founded by William Waldorf Astor.
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