Choice E is awkwardly written. "As interests rates" does not not contain a verb, so we do not know what they have been doing, even though the sentence is trying to get across that the rates have been rising along with the consumer and producer prices.

Choice B says "as have interest rates." Now we have the verb "have" and we know that the interest rates have been rising along with prices.

In E, comparison is between nouns, hence use "like", for clause comparisons, use "as". Hence incorrect.

why not A?

The problem with A, CD and E is that they have 2 clauses in different tenses. Only B has the correct tense

(A) Similar to rising interest rates, consumer and producer prices have been rising. present continuous--------present perfect
(B) Consumer and producer prices have been rising, as have interest rates.
(C) As interest rates are rising, so have consumer and producer prices. present continuous--------present perfect
(D) Consumer and producer prices have been rising, like interest rates do. present perfect and present. Also the use of Like is incorrect to comapre clauses
(E) Consumer and producer prices, as interest rates, have been rising.
E would be correct if "Like" would have been used.

thanks