What does paying extra buy you?
Why the saving is so large
Every extra dollar goes straight at the principal, and principal is what the interest is charged on. Early in a mortgage almost all of a normal payment is interest, so an extra payment in year three removes far more interest than the same payment in year twenty. That is why the interest saved is usually several times the extra you actually pay in.
The months saved come off the end of the loan, not the beginning: you keep making the same payment, and the term shortens.
Before you do it
Paying down a mortgage is a guaranteed return equal to your rate. If your cash earns more than the mortgage costs, prepaying it loses you money — a 2.75% loan against 4% savings is worth keeping. Check the rate on your cash first. Some mortgages outside the US charge a penalty for early repayment, which can be more than the interest saved.
This is principal and interest only. Escrow, insurance and PMI are not in it.