(A) In hoping to restrain economic growth, interest rates were raised by British policymakers, making it more expensive to borrow for businesses and consumers.
1) Modifier error: "Prepostion + V_ing", an opening modifier, modifies the immediate subject of the clause. Likewise, "
In hoping to" modifies "
interest rates", suddesting that "interest rates were hoping to...": illogical meaning
(B) Making it more expensive for businesses and consumers to borrow, interest rates were raised by British policymakers, in hopes of their restraining economic growth.
1) the same modifier issue as in A
2) even if we rectify the above-mentioned modifier error, we will not have a good sentence: although it is a myth that Gmat prefer "active voice" to "passive voice", I cannot see any good reason to use passive voice. I think that emphasis should be on WHO hoped, raised interest rates and thus made borrowing more expensive. So, I think that active voice works better
(C) In making borrowing for businesses and consumers more expensive, British policymakers, in hopes they will restrain economic growth, had raised interest rates.
1) Wrong tense: Past perfect is wrong because there is no timeframe or past action to show sequence.
2) "in hopes they will restrain...": to give the intended meaning, the sentence can be better constructed as the correct answer E
(D) Hopefully restraining economic growth, British policymakers raised interest rates, making more expensive borrowing by businesses and consumers.
1) Change in the meaning: The original meaning is that before or when British policymakers raised interest rates, they did not managed to restrain economic growth. Instead, They raised interest rates in order to retrain economic growth. D conveys the meaning that British policymakers were restraining economic growth immediately before or when they raised interest rates.
(E) Hoping to restrain economic growth, British policymakers raised interest rates, making it more expensive for businesses and consumers to borrow.
---"V_ing" modifies the suject of the clause and have some relationship with that clause: "Hoping to.." correctly modifies "British policymakers".
--- "comma + V_ing" usually modifies the nearest action and its agent, describing the main action, showing immediate consequence , or expressing simultaneousness. here, it shows immediate consuquence.