879 years, but the last ones expired in the year 1355.
However, because of the long-time span involved (878 years -- 35 generations!), there is plenty of time to improve our knowledge. If it is eventually decided 1950 DA needs to be diverted, the hundreds of years of warning could allow a method as simple as dusting the surface of the asteroid with chalk or charcoal, or sending a solar sail spacecraft that ends by collapsing its reflective sail around the asteroid. These things would change the asteroids reflectivity and allow sunlight to do the work of pushing the asteroid out of the way.Now the question has to be asked: Is there enough solar wind and time available to sprinkle Hillary with chalk and divert her trajectory from 1600 Penn?There is no reason for concern over 1950 DA. The most likely result will be that St. Patrick's Day parades in 2880 will be a little more festive than usual as 1950 DA recedes into the distance, having passed Earth by.