Look at the interest rate. Now look at inflation (not "core" inflation, the one you pay). Saving, money in bank, is not a good investment atm. Or put differently, it's at best as good as gold bars under the bed.
So yes, you not only have to save the money. You need to invest it.
I was not going into explicit detail, but pontificating on the idea of saving as opposed to spending.
With that said, one of my banks offered me a 3.00% APY on a CD the other day. Still not really enough for me. I would prefer to throw the money in index funds and wait longer.