I've never really paid attention to APR until I had to recently charge more than I could pay in full, due to buying a new house and needing to buy so many things. I decided to give the chat on AMEX's website a try. I successfully got them to reduce from 18.24% (originally 17.24% when opened) down to 16.24%. Later in the day, I noticed an offer for a card at 13.24% in my account. I called up and inquired about it, but found out it was a business card. I asked if they would match the APR. I was put on hold for a few minutes and she came back with saying she could lower my APR to 15.24%, saying that's the cap to how much they can lower a card in a single day.
I decided to call Discover and they also lowered my APR by 2%, and gave me a 12 month 0% interest offer as well.
TLDR; AMEX BCE reduced from 18.24% -> 15.24%, Discover IT Chrome reduced by 2% (can't remember the APR's, but much higher than AMEX)
