I am not an English native speaker, but I think that "I go home" is the commonly accepted idiom to say "I go to the place where I live". "I go to the house" does not mean exactly the same, it rather means that you go to "some specific house" that you and your interlocutor just happen to know.
I found this in some book: "Masculine and neuter nouns of one syllable may take an optional -e ending in the dative singular. Although this ending was once a grammatical requirement, it has become much less common. Today, the -e ending sounds old-fashioned and is limited to certain common idiomatic phrases and extremely formal and poetic utterances."
To make this easier for you:
Geographical means places that have names; eg. France, Berlin, Paris, County, etc.
Nach = To (Geographical, Compass direction) Ex. Wir gehen nach Brazil (We go to Brazil). Ex2. Wir gehen nach dem Osten (We go to the east). Exceptions: Nach Hause is a German Idiom meaning "To Home". There are more idioms like such.
Zu(m/r) = Too, To (Non-Geographical). Ex. Das ist zu viel (That is too much). Ex2. Kommst du zum Bau? (Are you coming to the building?) Ex3. Ihr geht zu uns! (You go to us!)
Note that for Zu: Zum - Is used for masculine words. Zur - Is used for feminine words. Zu - Is used for neuter words.
Nach Hause is an idiomatic phrase
http://german.about.com/library/weekly/aa061900a.htm that's a very good page to read more up about nach and zu
that pages goes into more detail about nach and zu...it's very good and helpful
In this sentence "nach" doesn't define the point in time, but where you are going (to). It becomes clearer in a different English sentence: I am going to school. Usually you would use "zu" as a translation for the "to". But for home you have to use "nach". Maybe it helps to remember that in English it is different from the norm as well: you just say "I am going home", not "to home".
Ich gehe nach Hause is present tense, but can refer to the immediate future.
The "nach" you were thinking of (my guess) can express that something happens after something else, which is why it refers to the future: "Nach dem Mittagessen spielen wir." - 'After lunch we (will) play.'
The English speaking people just go like this - Bam! - and they are home. Stong love, fast movement, no time for "to". Putting the joke aside - if you are not a native English speaker, like I'm not, it'd surely seem strange on first sight. But you get used to it. Well, maybe you could use "to" in some cases - "I am going to the home of..." but I'm not quite sure. However, the sentence in this exercise is refering to the speaker's home, not someone else's, so you just drop the "to".
- In English you should put a/the in front of the noun - "I go to a/the house".
- By using a/the house you'd mean you're going to a house which is not your home.
- "I'm going home." means you are going to your home, that's the best translation of the sentence in this exercise. Maybe "I'm going to my home" would have the same meaning, though.
Isn't this sentence grammatically incorrect? I believe that it should be "Ich gehe zu Hause." Nach is only used when geographical places are used, such as "Ich gehe nach Deutschland." (I go to Germany). Otherwise, if it's general, it's zu, ei "Ich gehe zum Hause" or "Ich gehe zur Schule".