Charge for idle EIP for IP addresses that you own

No, to ensure efficient use of Elastic IP addresses, we impose a small hourly charge when these IP addresses are not associated with a running instance or when they are associated with a stopped instance or unattached network interface. There is no charge for Elastic IP addresses you create from an IP address prefix you brought into AWS using Bring Your Own IP. Source: https://aws.amazon.com/ec2/pricing/on-demand/