Answer: I will save $40,000 by January 3, 2014, to use as a down payment on a home.
Explanation: SMART goals are:
Specific: they are well defined. Here, the goal is to save money towards the down payment of a house. It is clearly defined.
Measurable: it can be quantified with a number. The options, I will start saving money towards a new house does not state exactly how much. It can not be measured so it is impossible to say whether you have achieved the goal or not.
Achievable: It should be doable. We don't have enough information here to know if saving $40,000 by January 3 2014 is doable. For instance if the person setting this goal earns $80,000 per year and is setting this goal in 2012 or January 2013, it may be achievable. It is not if he makes $20,000 per year.
Relevant: the goal should be one that motivates you because it is important to you.
Time bound: There should be a time by which you want to achieve the goal.
The chosen option is the best goal of the because it meets more of the SMART goals criteria than the others: It is Specific, Measurable and Time-bound.