RDS is very expensive. Just following the console's advise for production instances (meaning Multi-AZ with a Proxy), a t3-medium (2 vCPU, 4GB) Postgres instance with 5GB storage is $130/month.
You can get it down to $12/month by going with a t4g.micro (2 vCPU, 1GB RAM), single-az, no proxy, no backups, 5GB storage; with price after that scaling roughly linearly with RAM. But the interface will scream at you the entire time that this isn't reasonable for a production setup.
You can get it down to $12/month by going with a t4g.micro (2 vCPU, 1GB RAM), single-az, no proxy, no backups, 5GB storage; with price after that scaling roughly linearly with RAM. But the interface will scream at you the entire time that this isn't reasonable for a production setup.