how much per hour do I have to pay for a stopped instance?

Hi Martin - Stopped instances accrue charges at the same rate as running instances. The reasons for this are addressed in our Billing Guide.

Charges will accrue for any service present on an account, even if it is powered off or otherwise not actively being used. This includes Linode Compute Instances that have been powered off as the data is still maintained and resources (such as RAM and network capacity) are still reserved. To avoid additional charges for a service you no longer need, remove the service from your account.

To see how much a server costs, you can check out our Pricing Page. Please note there are links to the pages for 2 data centers that have different pricing structures on that page if you need them.

If you want, you can take steps to Stop Further Billing by removing the server. Before you delete any services, you have options for saving the data, such as capturing an Image which can be stored for $0.10/GB per month. You can then deploy that to a new instance later. Or you can retain data locally by copying a disk over SSH.