A.the Federal Reserve Board needs to lower short-term interest rates further for stimulating
Use of "for" + gerund is incorrect replacement for infinitive of purpose (reason for verb).
B.the Federal Reserve Board needs to lower short-term interest rates further in order to stimulate
Correct.
C.the need is for the Federal Reserve Board to lower short-term interest rates further for stimulating
Unclear what need it is referring to.
D.there need to be a further lowering by the Federal Reserve Board of short-term interest rates for the purpose of stimulating
S-V agreement. "There need" should be "There needs" since "There" refers to gerund "lowering."
E.short-term interest rates need to be lowered further by the Federal Reserve Board so as to stimulate
Passive voice not preferred. I feel like "So as to" is not correct here, but I'm not sure why.