We can first calculate the monthly interest rate by dividing the annual interest rate by 12:
Monthly interest rate = 20% / 12 = 1.67%
Each month, Frank's balance will increase by the monthly interest rate, and decrease by the amount he pays. So, we can set up the following equation to find how many months it will take him to pay off the balance:
2000 * (1 + 0.0167)^n - (200n) = 0
where n is the number of months.
Simplifying the equation, we get:
2000 * (1.0167)^n - 200n = 0
Using a spreadsheet or trial and error, we can find that it will take Frank approximately 11 months to pay off the credit card balance.