how long does homemade sugar syrup last in the fridge?

Thanks both davidpdx and Shuna Lydon, esp for what mold looks like here.

Depending on how thick your simple syrup is, and how you cooled it down, and the vessel in which you store it in, and how cold your fridge is - these are the factors that contribute to your syrup's longevity. Simple syrup mold will often look like cloudy streaks in the liquid - make sure to taste before stirring or adding to anything.

There are too many variables for a precise answer. I have had simple syrup last from weeks to many months. You will know it has gone bad if you see mold or it has a funky smell. Bottom line: it is so easy and relatively inexpensive to make, just make an amount you would reasonably use in a few weeks. I store mine in the fridge in a sterilized screw-top bottle.