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These are actually almost impossible questions to answer because there many different factor involved in how much you will pay, mainly, how good are the windows, how well insulated is the building, are you on the top floor, middle floor or bottom floor, what type of heat, etc.
When my husband and I were first married we rented a 2 bedroom apartment, similar size to what you are looking at. We had electric heat and it ran about $50/month extra in the winter--this was a long time ago too. One move we had we rented a 4 bedroom townhome with a finished basement 2500 sq feet. It had gas heat and our HIGHEST gas bill there was $70. We have had friends that have had gas bills in the $500+ range renting small houses of about 1000 sq feet.
If you know who provides the utilities to the building, which company, usually you can call them and find out what was spent in the past couple years. Some companies will break it down by months others will give you a total cost for the year and then you just have to average that out. That is the best way to figure out a budget.
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