I am currently installing a Single Phase 240 volt 200 amp 3wire service on a residential
Home. The breaker box will be located approximately 100' from the utility meter. The copper wire will be ran underground 2'. What size wire will I need to run without having more than a 3% Voltage Drop?

3% of 240 volts is 7.2 volts dropped. #2/0 copper wire will give 3 volts dropped if the service is loaded to 80%.