The computing power of a human brain is estimated at 1016 cps (calculations per second). Neurons in the brain fire slowly but make up for their lack of speed with massively parallel processing. Computer power is growing exponentially, doubling every few years. Some say that the rapid growth of computing power will come to an end, but I disagree. The theoretical limit of computing according to the laws of physics is very high: a laptop having 1 kg of computing hardware can perform up to 1050 cps. Thus the theoretical limit of even a laptop is greater than the computing power of all of humanity.
By 2020 we should have super computers which have as much processing power as the human brain. By 2030 we should have laptop computers with as much processing power as the human brain. By 2050 we should have a computer which has as much computing power as all of humanity.
With so much computing power in a computer it is inevitable that a computer will pass the turing test. Computers will be intelligent enough to fool people into thinking they are human. Computers and robots will take over routine and physical tasks.
Humans will have a life of leisure as robots become their willing servants. Despite being humanly intelligent, computers can be programmed to follow human orders. This will definitely happen sometime in the late 21st century.
"Imagination is more important than knowledge" - Albert Einstein