A month has four weeks, so there are 4*4= <<4*4=16>>16 weeks in four months.
Since the tree grows for five centimeters every two weeks, it will grow by fifty centimeters every week for 16/2 = 8 weeks.
The tree will increase in height by 8*50 = <<8*50=400>>400 centimeters after four months.
Since 1 meter equals 100 centimeters, the tree is currently 2*100 = <<2*100=200>>200 centimeters tall.
After growing by 400 centimeters for four months, the tree will be 400+200 = <<400+200=600>>600 centimeters tall.
#### 600