This calculator gives the difference between two scenarios:

• Paying the minimum payment on your mortgage, and investing the difference under the risk-free rate (4-week Treasury Bill, with month-by-month data from treasurydirect.gov)
• Paying the whole amount entered above into your mortgage each month

The second scenario pays off the mortgage quicker (in the more conventional approach). The first scenario pays off the mortgage slower, in return for a potentially higher return. This is til the second scenario finishes, then it pays down the rest of the mortgage using the tbills.

This doesn't account for mortgages with variable rates, prepayment fees, etc. Also, tbill rates in the future are only a projection using today's rate.