Currently, the 7 day travel card costs 4950 forints.
And that entitles you to unlimited travel on buses , streetcars, trams, the underground, trolleys , cogwheel even local trains within Budapest ! If I am not mistaken you may also hop onto certain public boats by the Danube too but since I didn't try that out, can't confirm it.
Should you take the monthly pass, that would require a passport sized photo ID which you can easily snap at a mobile photo booth for around 1000 forints.
Here's a complete list of prices. The Hungarians thought of everything. There are even dog and bicycle passes.
The city is huge . I could have rushed it from the get go but I chose not to because no way, I hate that.... that's not the way I wanna travel. As a result, I did not get to ride the cogwheel . No matter, I was having too much fun exploring the city itself and this way, the memories do stick !
However, the week long pass did accord me rides on one of the world's oldest electrified subway line in the world ....
see the leather holders.