Do you charge for Shut down instances?

Yes, instances in a ShutDown/Shutoff state continue to reserve dedicated system resources (RAM, SSD storage, Floating IP, CPU) and therefore incur charges until you delete the instance. If you wish to no longer accumulate charges for a virtual machine, please use the Delete instances button in the dashboard.

If you want to use your instance in the future you can create a snapshot, follow this tutorial: How to create and restore an Instance Snapshot.