You can stack a new mattress on an old one so that it becomes a bed. This way, you don't have to get rid of the old one. But if you keep buying new mattresses, you are going to end up like the Princess and the Pea.
Back when I was a kid, and even as a young adult, the one who delivers the new mattress would dispose the old one for you -- without additional payment. Perhaps he could make a few bucks out of selling old mattresses to someone. But these days, nobody wants old mattresses -- I gather.
Well, actually a few years back, I got a new mattress. And the delivery man after much persuasion, grudgingly said he would throw the old one for me. A few hours later when I went downstairs to the provision shop, I saw it propped up against the wall, in the void deck. Horrors!
So, old mattresses really have no value these days. They don't even get stolen. What happened to those people who stole door knobs in broad daylight? (I was told by my banker friend that his mum came home one day but couldn't open her door because the door knob was stolen.) There were also those who stole grills from drains or pry out tyre rims to sell. There are a lot of springs in mattresses which are made of metal and they are welcome to plunder these.
Moral of the story, if you need to buy a mattress -- buy one that lasts forever -- or buy one of those light ones made of foam and about only 3 inches thick -- which you can carry down to the void deck. Oh, ok, to the garbage dump.
It is always useful to live near a garbage dump as I can foresee lugging a mattress, even if it is a thin and light one made from foam, is going to be quite a drag.