Hate to break it up to you but bitcoin will never reach it's limit of 21 million coins and there's some kind of a computation for this already in some thread which I'm too lazy to find.
Who says that? Why would it not be able to reach it? 20999999.97690000 should be mined according to the Wiki page, and that is close enough to say that 21 Million will be mined.
There are 100 or so bitcoins (don't remember the exact amount, but it's more than 50 and less than 200 BTC) that are permanently missing due to errors (accidental or intentional) by miners.
Therefore, Bitcoin will fall short by that amount from the theoretical 20999999.9769 limit.
The two main methods by which miners prevented the creation of these bitcoins are:
- Creating more than one generation transaction with the exact same hash.
- Failing to reward themselves with the full block reward they are entitled to.