It doesn't matter whether the comparison is made before-tax or after-tax. If you are comparing repayment of a 6 percent mortgage with acquisition of a 5 percent bond, for example, the before-tax comparison is 6 percent versus 5 percent. The after-tax comparison, assuming the borrower is in the 40 percent tax bracket, is 3.6 percent versus 3 percent. If mortgage repayment earns the higher return before-tax, it also earns the higher return after-tax.

What I failed to do in previous articles on this subject is distinguish two quite different situations: case 1 involves investing cash flows over an indefinite future period; case 2 involves investing a lump sum right now.

A young homeowner is most likely to be faced by case 1, where the question is how to allocate excess current cash flow. Should the cash be used to make additional payments to mortgage principal or to acquire financial assets?

The answer is that the owner should allocate excess cash flow to mortgage repayment if the mortgage rate is higher than the rate that can be earned that month on newly acquired financial assets. The owner confronts a new investment decision every month, and the action taken could change from one month to the next.

For example, the borrower with a 6 percent mortgage who has excess cash flow would do well to use it to pay down the mortgage balance if the alternative is investment in assets that yield 2 percent. But if two years down the road the same assets yield 7 percent, the borrower can stop allocating excess cash flow to the mortgage and start accumulating financial assets.

A senior is most likely to be faced with case 2, where the question is whether to liquidate financial assets in order to repay the entire loan balance. The owner makes a single investment decision that is irrevocable. Either the assets are liquidated to pay off the mortgage, or they aren't.

While the principle, that the decision should be based on comparison of the mortgage rate and the investment rate, is the same, the borrower can't adjust to future changes in the investment rate. He has to look ahead and anticipate what these changes might be. He also has to anticipate how long he will be around. 

To help deal with this problem, I developed a spreadsheet that allows a borrower to enter any scenario for future interest rates, and compare his wealth in every future month in the two cases: where he liquidates his assets to repay the mortgage at the outset, and where he retains both the mortgage and the assets. The spreadsheet is available on my Web site.

For example, assume the mortgage rate is 5 percent while the current investment rate is 3 percent, but the borrower assumes that in two years it will jump from 3 percent to 7 percent, and stay there. The spreadsheet shows that for the first 51 months, the borrower's wealth would be greater in the case where he repaid the mortgage. After 51 months, his wealth is greater in the case where he didn't. The borrower then must decide whether he is likely to be around for more than 51 months.

In general, the sooner that interest rates increase, the larger the increase when it happens, and the longer the borrower expects to live, the weaker the case for liquidating assets to pay off the mortgage. Seniors having to make this decision may find it instructive to play with the spreadsheet.