You should invest money in whatever pays the highest rate of return, obviously.
Some people want to be "debt free" and all, and in a typical interest rate environment that could make a lot more sense, but not at these rates.
We've seen several of these threads.
So at expense of repetition, the decision is driven by anticipation of inflation rates over life of the loan, mortgage deductibility (continued as policy or not), and how the individual plans to use monies otherwise tied up in paying off a home.
Financial Plans - Advice here is predicated on assumption that in not paying off mortgage, preserved liquidity is used for savings/investment rather than spending.
Deductibility - Addressed well with foshizzle's "ROI = 3.25 x (1 - 0.75) = 2.4%" equation above.
Inflation Hedge - If one expect's inflation rates to rise, a low fixed rate mortgage is an excellent hedge (self-explanatory). If one expects rates to decline, owning fixed debt at present cost would not be as helpful.
IMO, risk of inflation is significant. Image: http://www.lewrockwell.com/orig9/total_debt_to_gdp.png
Historic interest rates. Image: http://www.aboutinflation.com/_/rsrc/1320834310546/inflation-rate-historical/us-inflation-rate-historical-chart/US_Inflation_Rate_Historical_1956_2011.png
This post was edited on 1/3 at 4:01 pm