Here is a different approach using two solve blocks, one with odesolve, the second with find.
I get a different value for the resistor (785.57 ohm, compared to Fred's 710.94 ohm) , though, haven't checked why.
EDIT: Just used the easy to find exact solution of the ODE and found the correct value for the restistor again with 785.57 ohm! Not sure whats the problem in Fred's sheet.
EDIT2: Found the problem in Fred's approach. It was a simple precison problem because of the rather small time values used. Match() would find a couple of matches within the given tolerance and the first one of this list is not the best one. See my other reply to Fred's post for details and solution.