Learn Hardcore Russian: Бухгалтер проверяет финансовые отчёты каждый месяц. - The accountant checks the financial reports every month.

Russian does not have articles like English the or a/an. Definiteness and indefiniteness are understood from context, word order or additional words. In this sentence, you know which accountant we’re talking about from the situation, so no article is needed.

Why is проверяет used here (present tense) if the action happens each month?

In Russian, the present tense of an imperfective verb (like проверять) can express habitual or repeated actions (“every month”). If you said проверяет, it means “checks habitually/regularly.” A perfective form (проверит) would refer to a single completed action in the future, not a repeated one.

What is the form проверяет, grammatically?

Проверяет is the 3rd person singular present tense of the imperfective verb проверять (to check). Its full conjugation in present tense is:

я проверяю
ты проверяешь
он/она проверяет
мы проверяем
вы проверяете
они проверяют

Why do финансовые and отчёты both end in -ые and -ы, respectively?