+1
You should have X months living expenses in liquid reserves, where X is determined by your job security and tolerance for risk. This is not an all or nothing proposition.
Determine X, keep it in the bank, put the rest towards the mortgage.
Yeah, the numbers would probably say do a refinance, invest the $41k.. blah blah blah. The reality is it's $41k. If you net an extra 1% return on that over having used the money to pay off the mortgage, you'll clear a whopping $410 dollars a year. No thanks, I'd rather have the peace of mind that comes with owning the home.
I qouted the above response because it is pretty much a duplicate of what I have to say.
An emergency fund is an absolute necessity for one to have at all times, particularly if you have accumulated some assets in life, because the more you have, the more you have to lose. The amount of your emergency fund should be determined by your income, your expenses, and other risks you face in life (job insecurity, etc.). After you have taken out x dollars to put into a separate emergency fund account in a money market or a very, very conservative bond fund, contribute to whatever is left of your 41k in the bank. At your rate of savings, you should have enough money to pay off your mortgage by the end of 2012. By the end of 2012, you will be in financial heaven because you will be debt free, and you will have a cushion of cash for any emergency that may pop up. After your home is paid off, DON'T TOUCH IT!! I say this because you will undoubtly be solicited by every loan shark (many disguised as banks) to use your home as an ATM for free. A free and clear home is something to be proud of and should contribute to your good health.
DO NOT play games with the lenders!! By that I mean, do not refinance, take out a HELOC or any other type of a loan, and be sure to adhere to the terms of your mortgage by paying your agreed upon monthly payment, not more or less. Refinancing or any other type of loan, including a "no cost" HELOC, will only cost you money. If you are working hard to be debt free, why would you want to give any more of your money to the banks? Besides, HELOCS can be cancelled at any time for no reason, sometimes as soon as your house has been appraised and the loan has been set up; I've seen it happen all too often. Do you see in the media the trouble that people are having with mortgage companies in this crisis, some of whom are beginning foreclosure actions on properties that they never even lent money on? And you are thinking of giving these morons employed by a lender more money each month and/or a lump sum of your hard earned money hoping that they will apply it to the proper loan account, reduce the balance, and charge you less interest
Good luck on that!! That is not a strategy for hard working, frugal people.
By the way, this answer comes from someone who was a former investment sales rep and mortgage salesman. My jobs were to encourage people to take out mortgages and invest the money. LOL