After reading this topic, I tried Mailgun. But it turns out that their free plan allows only sending emails to manually verified addresses (whereas the one I’m going to recommend to you doesn’t).
This paragraph is added after discussion to correct what I said above: No, that sandbox restriction will be removed once a payment method added. To subscribe to a Flex (Pay as you go) plan, you need to subscribe to Foundation Trial first, then downgrade to it. (Thank you again the friendly Discourse community:)
I then searched on the internet and found Mailersend. It’s super cheap. 
Their free plan include 12 000 emails without daily sending limits! And their UI is modern and simple. I just used it and it works perfectly, so I would like to recommend it to you guys. Give it a try 
Their marketing mail service MailerLite is also cheap.
This is not spam. Impressed by how it’s cheap, I’m here recommending them to you. 