Adam Smith has a $125,000 balance on 8 different credit cards. He plans to make monthly payments of $2200 until the balance is paid off. The interest rate on each of these cards is 17.5% p.a., compounded monthly. A letter in the mail informs Adam that he has been approved for a new credit card with a $125,000 balance and that he can transfer all outstanding balances to the new card. There is no fee for balance transfers and the interest rate in the new card is 5.5% p.a., compounded monthly. If Adam
accepts the new card and transfers his entire balance (i.e., $125,000) to the card and if Adam continues to make payments of $2200 per month, how many months sooner will he pay off his total credit card debt?
--SHOW WORK