Pick a role and a target level. The result shows right away: how many quests, how many days, and how many World Locks you need to set aside.
The first quest each day is free. The next ones cost 3,000, 12,000, 27,000 gems and so on.
The game picks the Roles Day role at random every day, so MiwaMiwa uses the average: about 2 bonus days a week (1 Roles Day for your role + 1 Jack of All Trades). The finish date is an estimate and can move a few days either way.