Over the long term (i.e. say 5 or 10 years, but especially 10+ years), yes, money invested in stocks and/or bonds should grow more than if it is in a savings account (caveat: that is in no way guaranteed, but if history is any sort of guide, that should be the case). However, in the short term (i.e. 5 years or less) there is no telling whether it will grow or not. That is because nobody can predict (at least with 100% certainty or accuracy) short-term moves in a stock or even in the markets.
So, the main risk is that if you invest the $6,500 in stocks and/or bonds, you may have less than $6,500 when you need the money. If you keep it in a savings account, it will not grow much, but you know that you will have at least $6,500 if, and when, you need it.
If you might need some, or all, of the $6,500 within the next few years (e.g. less than 5), I would suggest keeping it in the savings account. If your time horizon for the $6,500 is more than 5 years, then it may make sense to start investing it, as long as you are all right with the fact that at various points in time when you look at your account, you might have less than that $6,500 in your account.
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