We underestimated the time needed to prepare for this exam and now have to stay up late studying.

underestimated 是动词 underestimate 的过去式形式。underestimate 由前缀 under-（表示"不足、低于"）和动词 estimate（估计）组成，意思是"低估"，即"对...的估计低于实际情况"。