Calculating Charge on a Capacitor in a Circuit with a Switch

[Gillian]

For the circuit shown in the figure, the switch S is suddenly closed with the capacitor uncharged. After one time constant, the charge on the capacitor is closest to:

a) 2.0 mC
b) 0.74 mC
c) 1.0 mC
d) 1.3 mC
e) 0.00 mCRelevant Formulas
q = Q⋅(1-e^-τ/R⋅C)
τ = RC

My Attempt
q = Q(1-e^-τ/T)
q = (10⋅10^-6)(1-e^-1)
q = (10⋅10^-6)(1-.36788)
q = (10⋅10^-6)(0.632)
q = 6.32⋅10^-6 C = 0.00632 mC

I am not sure how else I would approach this problem. Any suggestions?

 

[Orodruin]

Q is not $10^{-5}$ C.