If i power off my droplet in twelve housrs everyday,and reboot it to run for 12 hours everyday,will i pay for half fee (2.5 dollar) every month?
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No, you will pay for the full 24 hours / month. You only stop paying for your droplet if you destroy it. You still pay in a powered off state because the resources (diskspace, ram, etc.) are being reserved for that droplet.
See Pricing & Billing FAQ
Am I charged while my Droplet is in a powered-off state?
Yes. Your diskspace, CPU, RAM, and IP address are all reserved while your Droplet is powered off. If you want to save a Droplet for future use take a snapshot of it and then destroy it. You’ll be able to create a new Droplet from the snapshot image anytime to bring it back online.