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Is it wise to invest small amounts of money short-term?
This is slightly opinion based. Is it appropriate to invest small amounts for short periods of time?  At your age and the time period, I would say NO. This is because although the index fund do return 6-7% on average, there are several times it blips and goes negative as well. Stock Markets in short periods like 6 months can be unpredictable. At times a downturn will remain stagnant for periods of 2-3 years before suddenly zoom ahead. If you are not to particular about the time when you need the changes done; i.e. the changes can in worst case wait for few years; then yes investing in Index fund would make sense.  Else you are well off keeping this in savings. Try CD's if they can offer better rates for such durations.