Transients in Capacitive Networks (The Charging Phase)
Your answers are wrong.  After 1, 3, and 5 time constants, the voltage is (assuming it started at 0, the problem didn't say but should have):


1:   12.64 V
3:   19.00 V
5:   19.87 V


I can see the error you are making, but I want you to think about this a bit.  What exactly is the meaning of the time constant?  How would it change the problem if the resistor were tripled to 300 &Omega;?  Does that effect the length of a time constant, the voltage after one time constant, neither, both?