Charging a capacitor. Calculations and PSpice simulation don't match
The switch is the main problem. I'm not 100% sure here but I see at least 2 problems with the switch:
1. The closing time is defined as 1s, not 0s as you expected (So actually the switch opened during your whole simulation)
2. The default resistance value of the switch is 1 MOhm. So the switch itself is similar to a big resistor and your time constant in this case is:
tau = R_sw * C = 1M * 50n = 50 ms
That's why it took about 250ms for Vc to reach Vs value