Your teacher is correct.
affect, n., is a feeling, an emotion (and the emphasis is on the first syllable). As a verb (emphasis on the second syllable) it is to influence (have an effect upon) or pretend (The song affects me; she affects an accent); see: effect. 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. (Thanks to American Heritage Dictionary for this one). Usually, when you affect a situation, you have an effect on it.
effect is a result (the song has an effect...); vb. is to bring about or result in (She will effect a change if...); verb is synonymous with produce. See affect.