Mortgage Payment Inflation

I had an interesting idea this morning when I was reading a Bogleheads post on paying extra on your mortgage. Basically, assuming you are doing a traditional fixed mortgage, your mortgage payments are going to remain pretty much the same throughout the term of your mortgage. However, inflation will take it's toll on the value of your dollar so the real cost of your payment each month will be decreasing. To compensate for that, why not increase your mortgage payment to keep pace with inflation?

For example, if your mortgage payment is $1000 in today's dollars, then 10 years from now you should be paying the equivalent of today's $1000, which at 3% a year is $1,343.92. All of your other expenses will be increasing at that rate, so why not force yourself to pay off your mortgage faster. If your relative level of income has remained the same, you won't notice the difference. Of course, if your situation has changed then the reduced relative cost of the mortgage payment is a great advantage and can help you get by.