Share your insights or perspective on the financial matter presented in the input.

Formula that predicts whether one is better off investing or paying down debt
you should always invest if your investment rate of return is higher   than your interest rate Your next line, about standard deviation is dead on.  There are too many variables to give an exact answer here, in my opinion. The main reason is that one variable isn't easy to quantify - One's risk tolerance.  Clearly, there's one extreme, the 18% credit card. Unless you are funding loanshark type rates of 2%/week, it's safe to say that 18% debt should take priority over any investments, except for the matched 401(k) deposits.  What I think you're talking about is something we've addressed here in multiple threads.  Do I prepay my sub 4% mortgage or invest? In this case, (and to Noah's comment) the question is whether you can expect a post-tax return of over 3% during your time horizon. I look at the return for 15 years from 1998-2013 and see a 6% CAGR for the S&P. I chose 15 years, as the choice is often one of paying a 30 year mortgage faster, as fast as 15. The last 15 years offer a pretty bad scenario, 2 crashes and a mortgage crisis. 6% after long term gains would get you 5.1% net.  You can pull the data back to 1871 and run CAGR numbers for the timeframe of your choosing. I haven't done it yet, but I imagine there's no 15 year span that lags the 3% target I cite.  What makes it more complex is that the investment isn't lump sum. It may not be obvious, but CAGR is a dollar invested at T=0, and returns calculated to T=final year. It would take a bit of spreadsheeting to invest the extra funds every month/year over your period of analysis.  In the end, there are still those who will choose to pay off their 4% mortgage regardless of what the numbers show. Even if the 15 year result showed worst case 3.5% (almost no profit) and an average 10%, the feeling of risk is more than many will want.