CAT 6 cable

Hi,

We are planning to move our office to a new location. The problem is, the new location has CAT 3 cabling. Since we have 10 years lease on the building, we want to have something that will last us for atleast 10 years so we decided to go with CAT6 cabling for the new building. My question is, if we rewire the new building with CAT 6 will our existing patch cords, which is for CAT 5e, still be usable with the CAT 6? Do I need to replace all my existing patch cords too?

Thanks!