Did I forget how old I am?

This sounds like a really stupid question but if I’m right, I’m not the only person who has done it.
If I was born in say, 1961, my first birthday was in 1962. So, I’ve been thinking I was 49 since last spring, but haven’t I really only had 48 birthdays?
Someone I know was born in 1950 and therefore has been thinking he’s 60, but hasn’t he only had 59 birthdays?
Tell me if I’m wrong. I would much rather wait another year for the big 5–0— if I can.