International Calls

I had signed up for the $19.99 International Plan Rate and was able to make calls only to the UK. I have family all over the world especially Africa. I thought with my plan, I'd be able to also call Africa but each time I tried, the calls wouldn't go through. I was told I needed to upgrade my plan to the $29.99 plan which I did but the problem persisted and each time I called customer service, I was told that the problem was from the #s I was trying to call. It can't be because I'm able to make those same calls from my AT&T cell phone and also from prepaid cards.

What could be the problem? I think it's my Verizon line