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I'm a fan of ARM if you are disciplined enough to pay a little extra each month, and the more - the better. I too think the interest rates are not going anywhere any time soon. I have an adjustable rate equity line of credit that has been 3.00% for so many years that I can't remember how long it's been, probably at least 5 years. The other factor is how much money you owe. The more you owe, the more you will save with the lower rate.
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I look at it as the more you owe, the bigger the risk of a ARM. If you have $10k on an ARM and interest goes up, it doesn't cost you much and if push came to shove, most people could get it paid off somehow. If you have $1 million on an ARM and interest goes up .25%, that is serious money. It's basically a high risk/high reward situation. The more money you borrow, the higher the potential risk and reward. I understand your logic though.
To the OP, say you have $100k with 13 yrs left. Payment at 4% fixed is $824 and at 3.25% arm it would be 787. If you take the $37 you save each month and apply that towards principle so your monthly payment would be the same if you were 4% fixed, you would pay it off 8 months early. Keep in mind, if you go ARM and interest goes up, you can no longer lock in that 4%. Chances are, interest isn't going to sky rocket but nothing is certain these days and a lot can happen in 13 yrs.
Another scenario would be, what if interest jumped and you were paying 5%. You could still afford the payment but it would be $873/ month. $49 more than if you had 4% fixed. If you made an extra $49 payment per month on your 4% fixed each month, you would pay it off 11 months early.
Finally, a 13 yr, $100k loan at 4% will be a total repayment of $128.5k. A 3.25% loan but making the same payment as the 4% would be $121.5k for the life of the loan. $7k is a lot of money saved but it's far from guaranteed money. Maybe you get lucky and run with the arm for a year or two and lock in 3.5% but maybe you get unlucky and don't get it locked in and end up paying 7% or more. Interest is cheap right now. There isn't a lot of room for it to go down. There is a hell of a lot of room for it to go up. Unless you are going to very agressively pay it off soon, no way in hell would I do the arm in your situation. Though I don't know your situation so it's tough to say. The biggest problem with arms in my opinion is when people use them because they can't afford the fixed rate payment. That is a disaster waiting to happen. Using an arm and aggressively repaying isn't necessarily a bad idea but still has risks. My advice is probably worth less than you paid for it.