Learn Hardcore Polish: Sprawdzę należność niezależnie od tego, czy wzrosła, czy spadła. - I will check the amount due irrespective of whether it rose or fell.

Because sprawdzę comes from the perfective verb sprawdzić. In Polish, perfective verbs do not normally have a true present tense. Their present-looking forms refer to the future.

So:

sprawdzę = I will check
sprawdzam = I am checking / I check from the imperfective sprawdzać

Here the speaker means a single completed act of checking, so sprawdzę is the natural choice.

Why is there no ja in the sentence?

Polish often leaves out subject pronouns when they are clear from the verb form.

sprawdzę already means I will check
so adding ja is usually unnecessary

You could say Ja sprawdzę..., but that would add emphasis, something like I will check.

What exactly does należność mean here?

Należność is a formal/business word. Depending on context, it can mean:

amount due
sum owed
receivable
sometimes more loosely payment due

It is not the most everyday word for money in general. It usually refers to a specific amount that is owed or payable.