Suppose you have a $$20,000$ balance on your credit card $($Card A$),$ which charges you a $21\%$ annual interest rate. You have an option to transfer the balance over to another credit card $($Card B$).$ Card B will give you a promotional $0\%$ interest rate in the first year. After that, it will charge you $26\%$ as an annual interest rate.

You are currently paying off $30\%$ of your outstanding balance every year. Which card enables you to payoff at least $$10,000$ of your balance faster? $($Hint: You can reframe this problem as a fund investing problem in which the interest rate on the card is the rate of return of the fund and the rate with which you pay off your card is the expense ratio of the fund.$)$

Suppose you increase your payoff rate to $40\%$ of your outstanding balance every year. Which card enables you to payoff at least $$10,000$ of your balance faster?