An alternative to using logarithms to determine the amount of time that it would take to pay off a credit card would be to use a spreadsheet to list the value of the minimum payment after each paymenet period for as many times as is necessary.
Suppose that you “max out” a credit card to its limit of $10,000 and plan on paying off this $10,000 balance by making minimum payments of $250 (no other charges will be made with this card as you plan on destroying it once the balance is paid off). On the 8th day of each billing cycle, an automatic payment of $250 will be made to the credit card company which processes and records it on the same day as the payment.
At the end of each billing cycle the finance charge is added to the balance to create the beginning balance of the following billing cycle with an APR of 17.64% . Assuming that the average daily balance method is used and that the billing cycle is 30 days in length, determine how long it will take for the credit card to be completely paid off by showing the beginning balance of each billing cycle and each finance charge up to (and including) the one where the card is paid off.
To clarify, the card will be considered to be paid off when the amount owed at the time that the payment is scheduled to be made is $200 or less (essentially meaning that it will be paid off during the first billing cycle where the beginning balance is $200 or less).