It shouldn’t be a surprise for a native English speaker. You also express future acts with the present continous tense.
I’m going to school tomorrow.
The Hungarian sentence is expressed with the only present tense we have:
Holnap iskolába megyek.
The Hungarian present tense is used to express future acts more often than the paraphrased future tense. If you know the present (with all its irregularities), you know the future!
Egy óra múlva elmegyek.
I’m leaving in an hour.
Are you coming with me?
Még két évig dolgoznak a gyárban.
They’re working at the factory for two more years.
-Jössz? -Nem lehet. Öt perc múlva találkozok a barátommal.
-Are you coming? -I can’t. I’m going to meet my friend in five minutes.
ACTS IN PROGRESS
You can give tenses a continous aspect with this adverb: ÉPPEN. It means right now, at the moment. However, it is not necessary to use it. The present, past and future tenses can express continuity by themselves. Generally speaking, Hungarian verbs have a continous aspect until you fit them with a verbal prefix that expresses completeness.
Continous: Olvasom az újságot. – I’m reading the paper.
Complete: Elolvasom az újságot. – I’ll read the paper through.
Contious: Nézi a filmet. – He’s watching the movie.
Complete: Megnézi a filmet. – He watches the movie.
You can add ‘éppen’ to the continous sentences:
Éppen olvasom az újságot. Éppen nézi a filmet.
However, sometimes you can add éppen to verbs with complete aspect, too:
A rendőr éppen megfigyeli a rablót.
The policeman is watching the robber.
It is possible because ‘megfigyel’ describes an action by itself, a new meaning is given to ‘figyel’ by ‘meg’. And it doesn’t really express completeness in this case. As I said, you don’t have to use éppen to express something in progress.
Note that when you ask a question, éppen is placed after the verb: Mit csinálsz éppen? When answering, it can be at the beginning of the sentence separated from the verb: Éppen a blogomat írom.
AND WE’RE DONE WITH THE PRESENT TENSE!