Why does it help me to pay off my mortgage faster?

You might have noticed on my mortgage calculator page after you’ve done a calculation that it has a paragraph at the bottom that looks like:

Did You Know…
If you paid just $40 a month more, you would have your mortgage paid off 54 months earlier? You’d save $20,797.14 in interest and your total payments would be $195,735.89.

I sometime get told that the above paragraph doesn’t make any sense (after all, if you owe $100,000, you owe $100,000, right?), so I thought I would explain what is happening.
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