First, the answer to your question is no.
Second, there will never be 21 million in existence. As a matter of fact, there will never even be 20,999,999.9769 in existence.
Because when there isn't very much of something, and people want that something, it INCREASES in value. This is how the law of supply and demand in economics works. For example: There will never be more than one "real" Mona Lisa painting. After that one painting was completed, did it become worthless?
Bitcoin is worth as much as it is right now because:
- There isn't very much of it
- The people who want it are willing to pay that much for it
- The people who have it are unwilling to sell it for less
How do any of those things change when all the bitcoins have been mined?
The exact date is impossible to know right now, but it will most likely be somewhere around the year 2104 (give or take a few years). Note, as I mentioned earlier, we will never actually reach 21 million. We will never actually even reach 20,999,999.9769.