Wow, you really think it will take that long? If it does get harder to mine wont less and less people think that its worth the electricity and stop befpre the end?
Yep...that is how they were built. They will keep halving the block rewards till 2140. You can read more on the basics here:
http://en.wikipedia.org/wiki/Bitcoin In addition to archiving transactions, each new ledger update creates some newly minted bitcoins. The number of new bitcoins created in each update is halved every 4 years until the year 2140 when this number will round down to zero. At that time no more bitcoins will be added into circulation and the total number of bitcoins will have reached a maximum of 21 million bitcoins.