My boyfriend lies about small things - is there a future in this relationship?

[Ivy]

I have known my boyfriend for almost a year now and he is 25 and I'm 23. In the beginning, I caught him lying about insignificant things; for example, he lied about not having a Facebook when we first met, then he mentioned a week later that he had a profile and I was like, "Wait, didn't you say you didn't have Facebook?" and he casually said, "I did? I don't remember."

Another instance is when I asked him why he never seriously dated in college. He said it was because he was poor in college and didn't have money to take out girls, so he had a lot of relationships with girls where it was purely sexual. Months later, on a different topic, he mentioned how he had a lot of money in college because he had a thriving business. When I called him out on what he said prior, he didn't recall and didn't have a reason as to why he lied. We later concluded it was because he didn't want me to know he was "well off". I was still bothered by it because originally I asked him why he didn't date, which had nothing to do with how much money he had. He chose to bring up the topic of money himself and lied about it, at that.

Among these two, there were also little insignificant lies that I have long forgotten. After a serious discussion, we agreed that if he ever lied to me again, no matter how big or small, this relationship would not work. This was around late winter/early spring of this year.

More recently, I was chatting with him online and he mentioned something and I asked him where he learned it. He said he learned in class in college and I asked what class because I had taken similar classes and never learned what he mentioned. He then said, "Fine. I learned it on "Entourage," the show." I asked him why he lied and he said he didn't know, it was a brain fart. After a long discussion, he said I was overreacting over something so small, that I was being stupid. He even said that he's having serious doubts in being in a relationship with someone who has as heavy of trust issues as I.

I told him that he wasn't helping to remedy the problem or give me a peace of mind. If he sincerely apologized and seemed genuine, and promised he wouldn't do it again, it would probably help. Instead he makes me feel like I'm the one at fault and blowing things out of proportion. He says, "It's not like I lied about cheating on you or something." I told him I don't care about what he lies about, it's the fact that he lies at all. If he lies about stupid things, what else could he be lying about? It makes me question his word in the past, current, and future; and he doesn't understand why it's a big problem if it's not a big lie, and I don't know how to help him understand.

In the end, he said he was going to bed and we would finish the discussion later. I don't know what to do now. Do I hold to our original agreement and break things off? Or stay? Is it worth it to stay? Is there even a future with someone who lies about small things and doesn't see the significance and understand how much it upsets me? If I stay, is there a possible way to solve this? Possible compromises?

Any advice or help would be greatly appreciated, thanks.
I forgot to mention the reason why he lied about not having a Facebook was because he felt that since we had just met (we met online), he didn't feel it was necessary in sharing something so personal with me.
He claims that he's never lied about big things and he never will, but he can't promise the same for little things. I asked if he lies out of habit and he said no. He said he just can't guarantee that he won't say something stupid or have another brain fart and say something that doesn't quite make sense. I don't know if this makes me feel any better though...