Here running on different hosting will cause latency.
If you are running on RDS, let's take db.t2.micro then $0.018 per hour or $12.96 per month for RDS. And if running on EC2, let's take t2.micro then $0.0126 per hour or $9.07 per month.
If your application is small, you could host both your database and application on the same machine.
For more read here.
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