This seems to be a question about risk. If you pay down the mortgage, you're actually investing at a rate equal to the interest rate on the property. Do you have one income or two? Could you pay the mortgage if you lost one of the incomes? If the answer is no, then you may have too much risk leaving the mortgage around just to try to get a few more percentage points. Keep in mind that even though the market around 10-12%, adjusted for inflation isn't that around 8%? But even assuming that the rates over time are high, that's picking a start and an end point and doing simple work math on it. If you have 100k invested and the value drops by 25% in one year, the next year it has to raise 33% just to get back to even. The two year aver might appear to be +8%, but your portfolio might not reflect a +8% return over the two years.

But putting that aside, let's say you get an 8% return. Depending on your tax bracket, that 8% might be 6% after taxes. It is true that 6% beats 2.875%, but that's probably variable and might go up at some point. In any case, you're looking at a 3.125% increase in your rate of return at a higher risk(someone loses their job) in this example. You have to determine for yourself your risk tolerance and whether you can withstand a job loss for a few months(or longer) and still make the minimum mortgage payments. If not, I'd suggest just killing off the mortgage.

Just a question. If you had a payed off house, would you take out a mortgage to do some investing in the market? It's kind of the same question, but in reverse. If your answer is no, then you are answering your question.

Brian