Mostly rent here is regulated in comparison to the operation and management cost of the property divided out into the amount of homes within, and then they add a little on top to make a bit of coin of course.
Here you can as well have an A or a B contract.
A contract: Pay deposit + 1 month rent upfront -> move in and pay your rent -> move out -> see renovation cost and clean up taken from your deposit, either giving you some back or giving you a bill for more.
B contract: Pay deposit + 1 month rent upfront -> move in and pay your rent -> housing association takes 10% of your rent and saves it for when you move out -> move out -> see renovation cost and clean up taken from your 10% saved pr. month pr. year -> if more is needed, they will take from your deposit, else they tend to pay out your whole deposit without an extra bill (Of course depending on your time living there).
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In Denmark, you have two ways.
Ownership: You own the place and may do what you wish if your wish is up to code with the regulations of the council/kommune/state. (Ownership: You pay your housing tax, management cost and the likes as if it was a house but without property tax and your insurance is less).
Share of ownership: Share of ownership has you following a strict set of rules within the building, such as what windows to use, what paint to use on exterior walls, what companies to use for certain tasks as well as you have to ask the other shared owners for permission for altering your apartment before you may apply for permission from council/kommune/state. (Commonly a shared ownership is cheaper than buying an apartment, as well as you sadly do pay a sort of rent).