Aws provide free tier for Postgres, MySQl,...
Free tier specs can be found here
Bascially, you get
db.t2.micro - 1GB instance
Information are clear. However, default configuration are not for free tier.
If you don't choose it correctly, you will end up with being charged (a lot).
First, go to services, search for RDS
Choose create new DB.
Don't choose Amazon Aurora. It's default option, it's very good but. It does not support free tier
When choosing non-Aurora. In the list of template, there is a new template for Free-Tier
Now you can see that the only option that you can choose is : db.t2.micro and Multi A-Z deployment is disabled.