Sum if following criteria match

Dear all ,

In the attachment you can find a dummy example of my problem ,that I want to simplify. I need to sum the amounts that are in column A , but based on the ratings (column B). On the right side you have the criteria bins. For example sum all values in column A if they are rated AA, AA- , AA+. Or sum values from column A if they are rated BBB;BBB+;BBB-;Baa. So the formula should sum only values that have this criteria and will place the sum in the appropriate bins on the right.

I have done this assignment by doing filtering and then summing up rating by rating but wanted to see how can I use formula in solving this.

Thanks for help,

Bjelinski