I think the answer to where you should stash extra cash depends entirely on when you might need it and what your tolerance is for risk.
If you're thinking about a place to stash some extra cash before you need to pay the rent or tuition, it would be wise to keep it in a very safe and accessible place, such as a federally-insured account with a bank or credit union. The downside with these ultra-safe accounts is that they won't earn very much in interest at today's low interest rates, but your money will be safe. It's also always a good idea to keep an emergency fund in a safe place like this, just in case you run into an unanticipated expense in-between paychecks.
If you're thinking about longer-term investments that might someday pay for a house, retirement, or other long-term goal, there are many options to consider across the risk spectrum. There are lots of on-line resources and calculators to help you figure out how much you might need to save on a monthly basis to achieve these objectives. And, it's often a good idea to consult with an adviser on topics like this, to make sure you're on track over time to achieve your goals.
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