1 - Do you have a full-time job that pays a decent salary?
2 - Do you have enough money after this purchase to manage household expenses?
3 - Are you over 21?😀
I'm a full time grad student with very tight budget constraints and I get 1 paycheck per year when I lead services for the Jewish Holidays. So when I decided that I needed to upgrade from my 933MHz G4 to a 2.8 iMac, I talked it over with my wife and I gave her a list of reasons for the purchase. I had planned to pay for the entire thing from my 1 paycheck. However, my lovely, generous wife would not allow me to do that. I ended up only using part of the paycheck for the purchase and my wife completely agrees that it was a great buy. Of course, the advantage I have is that I used to do Mac support for a living and am therefore the live in tech guy.🙄 My point is that if this purchase will not affect your ability to pay your bills and put food on the table, she should not have a problem with it.
Best of luck.
P.S. The RAM changing instructions that someone here linked to are not for the current iMac. It covers the early intel models that did have 1 GB soldered on the Mobo and maxed out at 3GBs. The correct link is... I have just been hunting for the correct link but can't seem to find it at the moment. However, be assured that with current iMacs, you can absolutely replace both memory sticks.