How can I discuss plans to move out with my parents?

I am 24 years old, just finished school a few weeks ago from a good state univeristy, and finished with 2 Master’s degrees (Master’s in Engineering and an MBA in 6 years with a year of working experience to boot). I have over $15,000 in the bank because I’m pretty frugal and I was on scholarships throughout all of college (very lucky - no loans either) - I understand that this is a very good situation I’m in and a lot of people would love to be in my situation. I don’t have a job yet because I didn’t want to mess with it because I wanted some time off after being a full time student for 6 years straight (summers included) - I’m currently in Florida for 3 weeks. My parents are adament about me staying home to save even more money for a good down payment on a house (they want me to stay for 2 years - 1 year at least!) - don’t want a home right now, but want one in about a year or so - condos are out of the question. I want to move out into a one bedroom apartment for some independence, financial freedom, have some more fun with friends, and the opportunity to have some privacy with my girlfriend - they won’t let her stay the night and the door to my room must always be open if we’re in there together. I never let my parents pay for much during college - they offered to pay tuition when it was needed, room and board, or rent for apartments I stayed in and I told them “no” every time. I just want to know how to approach the situation and if my parents are “hovering” too much and if they’re being unreasonable. I think they are, but they’re so stubborn and stuck in their ways that I have a feeling that there will be some hostile feelings when I break it to them that I want to move out. I also feel that they are lonely in an “empty nest” and want some company - kind of selfish. I agree that I will save about $9,000 for that year in an apartment that could go toward a new home, but I know I wouldn’t be nearly as happy as I would having a place to myself and being independent for once in my life. I’m 24, and old enough with enough money saved up and opportunities for good jobs that I should be able to be on my own. I don’t know where they’re coming from because they got married at 21 and 23 and were independent from then on out. I need some help and I don’t want to ruin the relationship I have with them - they will be VERY upset when I tell them my view. How should I approach this situation and do you all think they are being unreasonable?