My goal is to save $250k in 10 years. Is this possible to accomplish?

Hello!

I'm 20 and I just graduated with a Bachelor's in Computer Science (thank God for high school AP credits). I have a very uncommon goal for a young adult -- and that is to have $250k saved by the age of 30. I determined that $250k at that age is personally enough money for emergency savings, a down payment for a mortgage, a potential business I could start, a rental investment property, and some savings for retirement which should continue to grow until I retire in my 60s.

I landed a junior developer job two months ago and I make $40k. It's a bit tight considering I live in a fairly expensive city, but I'm making it work. Taxes and health insurance take away 30 percent of my income, so I'm left with about $2333 each month. About $1700 goes towards rent, groceries, and other bills. Here is my monthly budget:

Rent: $1000 (cheapest studio I could find)
Utilities: $150
Groceries: $220 (I know, not very easy)
Subway/Transportation: $120
Cell phone/Internet: $50
Misc./Clothes/Entertainment: $130

So that leaves me with approximately $667 to save per month. $8000 * 10 years is $80k by the age of 30. It's not enough. But then again, those savings aren't invested. Where should I invest the $667 monthly savings, and how much would I return in 10 years?

I'd like any advice you have for me!

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