What does "на" mean in expressions relating to time?

Question

This is somewhat related to a previous question of mine.

Question: What does "на" mean in expressions relating to time?

My guess had been that "на" used in expressions related to time somehow indicated that the action would occur after the amount of time in the accusative case following "на".

However, such expressions appear to also occur in the past tense, which seems to indicate my attempt at interpretation is incorrect.

The examples from my workbook are all sentences with perfective verbs. However, I don't think that could explain the meaning somehow, since that explains the difference between "за+accusative" and "accusative" for expressions involving time, unless "за" and "на" were synonymous in this context. That seems unlikely to me although I have no idea either way.

Some exercises from my workbook involve explaining the meaning of sentences involving "на" and expressions of time. Examples are below which hopefully can clarify what I am confused about.

На сколько времени вы приехали в Москву? Мы приехали в Москву на один год.

Он взял словарь на час. Он будет смотреть словарь час.

Они приехали в Москву на месяц. Они будут в Москве месяц.

Я взял книгу на неделю. Она взяла журнал на один день. Они взяли магнитофон на вечер.

Они приехали в нашу страну на полгода. Туристы приехали в Ярославль на неделю. Она поехала в санаторий на месяц.

Answer 1

First, the "verb + на" is equivalent to English "verb + for". In Russian, the verb is perfective in most cases, but not always.

Он взял книгу на неделю - he borrowed (lit. took) a book for a week.
Она уехала в Москву на месяц - she left for Moscow for a month.
Беру эту книгу на две недели - I borrow (lit. take) this book for two weeks.

If some action is done for its temporary consequences, the preposition на tells how long these consequences intend to last (NOT how long the action itself lasts, and usually not how long the consequences really last). For example, if one borrows a book, he/she does it in order to posess a book for a while. So на tells us how long he will posess a book. If one is imprisoned (Russian: он сел в тюрьму, or его посадили в тюрьму, or just его посадили), the authorities do it in order to keep him in prison for some time, so на tells for how long they intend to keep him in prison (его посадили на два года).

There is also навсегда - forever (i. e. он уехал из России навсегда), and на какое-то/некоторое время (i. e. я решил на какое-то время уехать в Индию).