It is the rule for this online forum that we will not allow to help anybody's homework. However, I'm tempted to help you with this one because I agree with your opinion. It seems that you have already given some thoughts to this question.
I believe that I heard it from somewhere that it is a general rule that we should never use "to" at the begining of the sentence. We may use it in the conversation, but the informal one. Therefore, I personally believe that "spending" is more appropriate for this sentence.
Student or Learner