مدة الإعارة شهر وتاريخ الاستحقاق غدا.

Because Arabic often omits the present-tense verb to be.

So instead of saying something like The loan period is a month, Arabic simply says:

• مدة الإعارة شهر
• literally: loan-period duration month

This is called a nominal sentence. In the present tense, the copula is/are/am is usually not stated.

If you wanted a past or future meaning, Arabic would usually use a verb such as كان or سيكون.

It is basically two nominal sentences joined by و:

1. مدة الإعارة شهر
   = The loan period is one month

2. تاريخ الاستحقاق غدا
   = The due date is tomorrow

The و simply means and.

It is an iḍāfa construction, often called a genitive construct or noun + noun possession structure.

So:

• مدة = duration / period
• الإعارة = the lending / the loan

Together:

• مدة الإعارة = the duration of the loan / the loan period

The same thing happens in:

• تاريخ الاستحقاق
• literally: date of the due-ness / due date

In an iḍāfa, the first noun is followed directly by the second noun, and the second noun determines the relationship.

Because in an iḍāfa, the first noun normally does not take الـ, even when the whole phrase is definite.

So:

• مدة الإعارة = the loan period
• not a loan period

and

• تاريخ الاستحقاق = the due date

The definiteness comes from the second noun:

• الإعارة is definite
• الاستحقاق is definite

As a result, the whole phrase becomes definite.

Here شهر means a month / one month.

Arabic often uses a bare singular noun in this kind of sentence to express a measure or duration. So:

• مدة الإعارة شهر
• literally: The loan period [is] a month

In English, we often naturally translate that as one month.

If you wanted to make the one extra explicit, you could say:

• شهر واحد

But in many contexts, just شهر is perfectly normal.

In fully vocalized formal Arabic, it would normally be شهرٌ here, not شهراً.

That is because شهر is the predicate of a nominal sentence, and a normal noun predicate is typically nominative.

So the fully vocalized form would be:

• مدةُ الإعارةِ شهرٌ

However, everyday printed Arabic usually omits case endings, so you just see:

• شهر

That is very normal in modern texts.

Yes—if fully vocalized, it is usually written غدًا.

In ordinary unvocalized text, Arabic often leaves off the diacritics, so you commonly see:

• غدا

This word means tomorrow.

Grammatically, غدًا is an adverb of time (ظرف زمان), so it is normally in the accusative form. That is why, in a fully marked version, you would expect:

• تاريخُ الاستحقاقِ غدًا

So there is a useful contrast here:

• شهرٌ = noun predicate
• غدًا = adverb of time

Yes, تاريخ can mean both history and date, depending on context.

In this sentence, it clearly means date, because the phrase is:

• تاريخ الاستحقاق

That is a common formal expression meaning:

• due date
• maturity date
• date when something becomes due

So this is one of those Arabic words whose exact meaning depends on the context.

Literally, استحقاق has the idea of something being deserved, owed, or due.

In administrative, financial, or library-style language, it often refers to the point when something becomes due.

So in:

• تاريخ الاستحقاق

the meaning is not something like date of deserving, but rather the standard practical meaning:

• due date

This is a good example of how formal Arabic often uses abstract nouns in set expressions.

A fully vocalized version would be:

• مُدَّةُ الإِعَارَةِ شَهْرٌ وَتَارِيخُ الِاسْتِحْقَاقِ غَدًا

A careful pronunciation is roughly:

• muddatu l-iʿārati shahrun wa-tārīkhu l-istihqāqi ghadan

A simpler learner-friendly pronunciation, without worrying too much about case endings, is:

• muddat al-iʿāra shahr wa tārīkh al-istihqāq ghadan

Both help, but the first reflects the formal grammar more accurately.