There was a big thread on the housing board on the Motley Fool(my favorite finance board) about this and Quiksand's explanation is indeed why you're paying down extra principal, you end up with a few extra payments a year. The general consesus from the mortgage wizards there was that there is absolutely no reason to do this, as you could just pay a little extra towards the principal on your own every month to get the same result.
The board isn't free but here are the relevant comments:
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I think that the biggest savings is from the fact that you make more
payments in the course of a year; 26 biweekly payments (equal to 13
monthly) instead of 12 monthly. It has been discussed quite a bit in the past,
but it basically boils down to that you can get about the same result simply
by making an extra payment each year. The general recommendation seems
to be to avoid this system if there is any fee associated, but you may like it
if you get paid biweekly. OTOH, if you go this route, there will be no
more "bonus months" where you get three checks, but have only two checks
worth of payments to make.
My preference would be to stick with monthly payments; if you get enough
money saved up and want to invest it at your mortgage rate, then you can
always (well, almost always) opt to pay extra towards principle. If you run
short, or find a better investment, then you still have the option of not
paying the extra. If you lock into a program, you lose the option.
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The benefit, as dcarper stated, it due to the extra payment you make over
the course of the year. If you like this idea, you can just as easily add 1/12
of a payment to each monthly check you submit and request that the extra
payment be credited to principle.
Also, this bit of info is from a mortgage broker who is well respected over on this board, interesting info:
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Mortgage lenders do NOT generally book loan payments according to when
they actually arrive... rather... as long as they arrive prior to their "late
payment deadline" the lender books ALL payments on a standardized day of
the month. Paying early provides no savings benefit to the payer.