Is the use of present perfective necessary?

In the sentence, "It has been many hundreds of years since people have believed in the myths of the Greeks and Romans, yet you can see that they still echo in our minds and in our language."
Is the present perfective necessary? Is it Ok if the sentence is written as "...since people believed in ...".
If this sentence is also correct, then what's the difference between the original one and this one?

Where did you get present perfective from? It's present perfect.

The simple past ("...since people believed in ...") is more grammatical.

Rover

That's the third time you have posted this question, chance 22. Please post a question only once, and be patient. If your question has not received a response after six or seven hours, then just bump it. Don't post it again; this can cause confusion.

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Originally Posted by Rover_KE

Where did you get present perfective from? It's present perfect.

The simple past ("...since people believed in ...") is more grammatical.

Rover

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Thank you Rover. In our English grammar coursebook, it's referred to as present perfective, so I just took it for granted.

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Originally Posted by chance22

Thank you Rover. In our English grammar coursebook, it's referred to as present perfective, so I just took it for granted.

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Your coursebook is wrong.

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Originally Posted by 5jj

That's the third time you have posted this question, chance 22. Please post a question only once, and be patient. If your question has not received a response after six or seven hours, then just bump it. Don't post it again; this can cause confusion.

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Sorry, I think there's something wrong with the network. Each time I submitted the thread, the page would finally become blank and I didn't know whether it's available or not. The same happens when I try to open a foreign website.