Effect and affect are two of my favorite words to use properly. Both can be used as either a noun or a verb but they are not in any way interchangable, as this usage note explains.
Affect and effect have no senses in common. As a verb affect is most commonly used in the sense of to influence (how smoking affects health). Effect means to bring about or execute: layoffs designed to effect savings. Thus the sentence These measures may affect savings could imply that the measures may reduce savings that have already been realized, whereas These measures may effect savings implies that the measures will cause new savings to come about.