Introduced in 1960s, reasons for modern credit cards’ popularity were convenience of use, less dependence on cash, and special discounts available only to credit card users.

(A) Introduced in 1960s, reasons for modern credit cards’ popularity were convenience of use, less dependence on cash, and special discounts available only to credit card users. -> Modifier error. reasons can't modify "Introduced in 1960s". Incorrect.

(B) Introduced in 1960s, modern credit cards were made popular because of convenience of use, less dependence on cash, and special discounts’ availability only to credit card users. -> Parallelism error. "convenience of use", "dependence on cash" and "special discounts’.....to credit card users" is incorrect.

(C) Reasons for popularity of modern credit cards, introduced in 1960s, were convenience of use, less dependence on cash, and special discounts available only to credit card users.-> We need Phrase +comma +Subject structure. Incorrect.

(D) Introduced in 1960s, modern credit cards have been popular because of convenience of use, less dependence on cash, and special discounts available only to credit card users. -> We have Phrase +comma +Subject structure in place. Further, "have been" means, it is till now. Meaning wise it makes sense. Let's keep it.

(E) Introduced in 1960s, modern credit cards were popular because of convenience of use, less dependence on cash, and special discounts available only to credit card users. -> We have Phrase +comma +Subject structure in place. Now, Meaning wise, we are saying, It was popular in last. Which is not the intended meaning.

So, I think D.

IMO D

Let's see what the sentence forms in Meaning Wise.

Something was Introduced in 1960s.
Then this sentence is followed by reasons why it was Famous.
Well this doesn't convey a meaning.

POE.

(A) Introduced in 1960s, reasons for modern credit cards’ popularity were convenience of use, less dependence on cash, and special discounts available only to credit card users. - MeM doesn't agree Logically.
Modified Entity and the Modifier are not forming a meaningful sentence
( X )

(B) Introduced in 1960s, modern credit cards were made popular because of convenience of use, less dependence on cash, and special discounts’ availability only to credit card users. - Were Made Popular is Wrong . Tense change and Meaning Change ( X )

(C) Reasons for popularity of modern credit cards, introduced in 1960s, were convenience of use, less dependence on cash, and special discounts available only to credit card users. - Modifier Error ( X )

(D) Introduced in 1960s, modern credit cards have been popular because of convenience of use, less dependence on cash, and special discounts available only to credit card users. - Modifier Introduced is modifying Modern Credit Cards.
Have Been Popular is the right use of Tense ( ✓ )

(E) Introduced in 1960s, modern credit cards were popular because of convenience of use, less dependence on cash, and special discounts available only to credit card users.
- Were Popular? No where it's written nor the meaning of the original sentence is Credit Cards were popular but they're not now
( X )

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