Baker? Sure, making cookies adds value to the world. Software? Yeah, writing programs adds something to the world. Holding onto money, lending some of it out, and taking a cut? Not so much.
That's slowly starting to happen in the financial industry, with robo-advisors and cheap index funds taking trillions of dollars out of the hands of overpaid Wall Street firms, but that process takes time. Hopefully we'll start to see the same thing with Lyft and Sidecar eating into Uber's nonsensical valuations.
When I pay him off, slowly, over time, and somewhat enrich him, nothing of value has been added to the world.
It's counterintuitive, maybe, but any sort of trade adds value to the world even though all that's happening is that goods and/or money are being moved from one place to another. What enables this is that different people have different preferences; in the case of your mortgage, it's differences in how you value future money relative to present money -- you want money now and having less money later is a cost you're willing to pay, whereas your mortgagee prefers to have more money later and doesn't mind having less now.
And so you make the trade -- in this case, you exchange a pile of money for some obligations to make future payments adding up to somewhat more money -- and both parties consider themselves better off than before. If that isn't adding value to the world, I don't know what is.
It's not a very glamorous kind of added value: it's less exciting than inventing a new kind of machine, or shaping raw materials into beautiful sculptures. But added value it is.
(Assuming, of course, that you and the mortgagee aren't badly wrong about your preferences. If it turns out that you're going to be spectacularly unable to repay the mortgage, so that you lose your home and the mortgagee loses the money, then maybe everyone loses. See, e.g., 2008. But on the whole it seems like the existence of mortgages is a considerable net benefit.)
Nothing new is created when ownership changes hands, as in the case of me possessing the money to buy a house, where before I didn't.
A change of ownership, or a new contract that two people have signed, or a promise to do something, none of that adds value to the world. The value is in the doing.