Yes, it is correct. Why do you think that 'put' might be wrong?

"I have put 500 dollars into the box in the last three years." is more correct. "I have been putting money into the box for the last three years and have put 500 dollars away." Is it what you mean?

I wonder how often you put money into the box. Maybe you mean I have put 500 dollars into the box OVER the last 3 years. Maybe "I have been putting money into the box regularly over the last 3 years, amounting to 500 dollars". Your original "I have put "is fine too, no other form of PUT unless you change the tense to I HAVE BEEN PUTTING....etc.

Exactly. It's a correct sentence, in that it is grammatically sound and has a meaning. But it may not mean what you think it does! Looking at your responses to the answers below, I suspect that you have come up with a correct sentence by accident: it's a sentence which happens to be correct, but it isn't what you wanted to say.

Your grammar is fine, but your statement is ambiguous.