Which one is the cheapest to use AWS RDS or my own database?

I have wordpress application running on my EC2 - AWS. I haven't decide which one is Amazon RDS or my own database on different hosting. Which one is the cheapest to use? Let's say I have my own MySQL database from Lunarpages or Bluehost hosting, to allow my wordpress on EC2 instance to connect/remote to my database on Lunarpages not allow my wordpress to connect remote to Amazon RDS. Which one is the cheapest to use? I heard people saying when you use Amazon RDS is very expensive, so I thought maybe to save costs to allow my wordpress to connect to my own database not Amazon RDS for wordpress. I don't know it is true or not. I don't know how it performance well. Which one is the best one. Any suggestion appreciated. Thank you.

Running on a different hosting will cause extra latency.

Let's do the math on AWS RDS for the smallest instances (taking eu-west-1 region as example)

1. Running on RDS: db.t2.micro $0.018 per hour, or $12.96 per month for RDS. Free the first year under AWS free tier.
2. Running on EC2: t2.micro (You configure MySQL and backups, ...), $0.0126 per hour, or $9.07 per month. Free the first year under AWS free tier

If your application is small enough, you could host both your database and your application on the same machine (solution 2)