While I'm like the others in questioning your math, I also have other concerns. Why does your son want his Eagle so fast? What are his plans for after he receives his Eagle badge? Unfortunately I've seen this problem a lot where kids are into receiving their Eagle and not becoming an Eagle Scout. Where is the scouting?
How many camps has he attended? 50 milers he's hiked? What scouting experiences has he had that didn't = merit badge or rank advancement? Has he even had the chance to do leadership training or become a leader in his troop? This whole "I have to get my Eagle now ASAP" situation along with the "oh crud, I better get my Eagle before I turn 18 2 weeks from now" situation, is too common. It's so bad here that having an Eagle doesn't get you that extra edge it once used to (except in the military of course).
Becoming an Eagle Scout is more than just completing the requirements for a badge. It's about being a scout. 1 - 1 1/2 years is s only barely scratching the surface of becoming a true scout.
This month's "Ask Andy" article covers this topic very well. I wish you and your son the best of luck in your endeavors. I just ask that you take the responsibility of earning the Eagle rank seriously so that it does not jeopardizes those who do became an Eagle Scout.
(I hope it's okay to post a link - if not please remove).
http://netcommish.com/AskAndy51.asp