I am in a similar position , but i live 1 mile inside the North/South Circular , so when the zone is extended (originally scheduled for mid 2021) I would have to pay the charge every day.
My car is a little later than yours a 2006 model, which is Euro 4. If you put your reg number into the Transport for London website
(
https://tfl.gov.uk/modes/driving/che...-vehicle-35896)
it will indicate whether it is compliant. Mine is, so big relief.
Sorry did not see that this link has already been posted above.
My fun car, and my wife's car are not so we face a pretty big bill for renewing 2 vehicles which are still going strong and we planned to keep for many years yet.