I can pay $1200 extra once a year or $100 every month - which is better? The first one does sound better, but for a 30 year mortgage, is it that significant? Say the mortgage is for $200,000.
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In general, the earlier you apply a payment, the better, because future payments will include less interest and more principal (the mortgage balance is lower, so less interest has accrued). If you have the $1200 now, then it makes sense to put it on the mortgage immediately. However, if you'll have to save $100 per month for a year and then pay it on the mortgage, you'd be better off paying $100 per month straight to the mortgage.
From a purely fiscal point of view, you will be better off paying $1200 off upfront instead of $100 a month. This is because the money is in your account earlier which lowers the amount you have to pay in interest for that whole year.
To illustrate, you can go to this site.
Under these conditions
Loan Amount : 200,000 Interest rate : 6.5%
Under 12 $100 payments per year, you will save $55,945.77 and 5 years and 7 months in the life of the whole loan.
If you pay one $1200 payment every year, you will save $59,549.80 and 5 years and 10 months.
So you'll save about 4000 in 24 years.
The best strategy is to have 1 year of mortgage payments in savings. This way, if you get laid off, or some other even occurs that precludes you from being able to pay normally, you won't pay late, and you won't affect your credit.
Between the low interest rate and the tax credit, borrowing for a mortgage is very inexpensive. Only make efforts to pay off your mortgage early once your other debts are paid in full. Student loans also. They may seem to be of lower interest rate, but because you can't eliminate them in bankruptcy, they are very dangerous should something happen to your income stream.
Finally, as the others have said, it is most likely not significant.
You didn't offer the rate or balance. At 5%, the $1200 paid in january would put you to the better by $60. If paid over the year, $100/mo, you're $30 to the better that year. Either way, subsequent years produce a compounding on the $60 interest. To answer just your question - if your intent is to pay early, earlier is better.
Some banks have been known to mis-apply the extra payments, so regardless of what you chose to do, be sure you track your balance.
Keep in mind (this now veers off the original question) paying early is the choice to invest in a guaranteed fixed rate, for the remaining life of the loan. The rate of course, is your mortgage rate. I'm compelled to advise that you first be sure you are depositing to your 401(k) up to your company match, if any, then have all other debt paid off, and as others said, emergency funds saved. I've seen the crazy notion that "$100 to my mortgage will save me $400 at the end of my loan, but paying my 18% credit card only saves me $18." Nonsense.
In short, the earlier you make the extra payments, the better it is.
Here's a quick illustration of 5 extra payment scenarios using a 30-year $200K mortgage @ 5% interest rate starting from Jan 2013:
1) No extra payments : http://usmo.org/1zSdX3t
Total Interest Paid: $186,511.57
2) Pay $100 extra per month starting from the first month of your mortgage : http://usmo.org/1hYLfsF
Total Interest Paid: $149,442.54
3) Pay $1200 extra at the end of the year, starting from first year of the mortgage : http://usmo.org/19JnURO
Total Interest Paid: $150,787.53
4) Pay $1200 extra at the beginning of the year, starting from first year of the mortgage (unlikely scenario because you would probably include it in the down payment): http://usmo.org/1hYLYKo
Total Interest Paid: $148,087.12
5) Pay $1200 extra at the beginning of the year, starting from second year of the mortgage: http://usmo.org/1hYLwvP
Total Interest Paid: $151,024.59
6) Accelerated bi-weekly payment without extra payments
Total Interest Paid: is $152,154.98.