RDS Free Tier Showing Cost - MySQL Public IP

The console tells you what the costs would be IF you didn't have the Free Tier credit, or run more than one t2.micro during the month. This is a consequence of how the Free "Tier" works, which is poorly understood. The Free Tier isn't a special mode or type of instance in RDS, it is a credit that is applied at the end of the month if you are within your first year of the account's life. So during normal RDS operation it has no idea if an RDS instance is "free" or not. At the end of the month the billing system applies a credit of up to 750 hours of t2.micro time and 20GB of storage & snapshot storage to the account.

Since the RDS Console doesn't know the history of the account, or how to present all the complexities around application of the credit, it can't know that this specific free-tier eligible t2.micro will actually be free. What happens if you fire up two at the same time? You will only be charged for having one, but there isn't any identification in the system which one is free and which is charged for. So the console can't really tell you which one would be free and must display the estimated charges independent of the credit that will be applied at the end of the month.

I went and looked at creating a default Free Tier eligible instance in Mumbai and received the same estimated cost as in your example. So, assuming that is the only t2.micro instance you have in a month, you don't change the configuration (e.g., add more storage or turn on Multi-AZ), and you are still in the Free Tier portion of the account's life, it should be free.