I have a credit card that is charging me two different APRs, one for cash withdrawal and one for purchases. I am trying to determine how much I need to pay monthly to zero the balance, but most online calculators ask for one APR. How would I determine the "average" APR? I would enter the higher APR, but I only have a small balance left on that part of the debt, and I don't want it to skew the calculation.
@Joe's original answer and the example with proportionate application of the payment to the two balances is not quite what will happen with US credit cards.
By US law (CARD Act of 2009), if you make only the minimum required payment (or less), the credit-card company can choose which part of the balance that sum is applied to. I am not aware of any company that chooses to apply such payments to anything other than that part of the balance which carries the least interest rate (including the 0% rate that "results" from acceptance of balance transfer offers). If you make more than the minimum required payment, then the excess must, by law, be applied to paying off the highest rate balance. If the highest rate balance gets paid off completely, any remaining amount must be applied to second-highest rate balance, and so on. Thus, it is not the case that that $600 payment (in Joe's example) is applied proportionately to the $5000 and $1000 balances owed. It depends on what the required minimum payment is.
So, what would be the minimum required payment? The minimum payment is the total of (i) all finance charges incurred during that month, (ii) all service fees and penalties (e.g. fee for exceeding credit limit, fee for taking a cash advance, late payment penalty) and other charges (e.g. annual card fee) and (iii) a fraction of the outstanding balance that (by law) must be large enough to allow the customer to pay off the entire balance in a reasonable length of time. The law is silent on what is reasonable, but most companies use 1% (which would pay off the balance over 8.33 years). Consider the numbers in Joe's example together with the following assumptions: $5000 and $1000 are the balances owed at the beginning of the month, no new charges or service fees during that month, and the previous month's minimum monthly payment was made on the day that the statement paid so that the finance charge for the current month is on the balances stated). The finance charge on the $5000 balance is $56.25, while the finance charge on the $1000 balance is $18.33, giving a minimum required payment of $56.25+18.33+60 = $134.58. Of the $600 payment, $134.58 would be applied to the lower-rate balance ($5000 + $56.25 = $5056.25) and reduce it to $4921.67. The excess $465.42 would be applied to the high-rate balance of $1000+18.33 = $1018.33 and reduce it to $552.91.
In general, it is a bad idea to take a cash advance from a credit card. Don't do it unless you absolutely must have cash then and there to buy something from a merchant who does not accept credit cards, only cash, and don't be tempted to use the "convenience checks" that credit-card companies send you from time to time. All such cash advances not only carry larger rates of interest (there may also be upfront fees for taking an advance) but any purchases made during the rest of the month also become subject to finance charge. In other words, there is no "grace period" for new charges, and this state of affairs will last for one month beyond the first credit-card statement whose statement is paid off in full in timely fashion.
Finally, turning to the question asked, viz. " I am trying to determine how much I need to pay monthly to zero the balance, ....", as per the above calculations, if the OP makes the minimum required payment of $134.58 plus $1018.33, that $134.58 will be applied to the low-rate balance and the rest $1018.33 will pay off the high-rate balance in full if the payment is made on the day the statement is issued. If payment is made later, but before the due date, that $1018.33 will be accruing finance charges until the date the payment is made, and these will appear as 22% rate balance on next month's statement. Similarly for the low-rate balance.
What if several monthly payments will be required? The best calculator known to me is at https://powerpay.org (free but it is necessary to set up a username and password). Enter in all the credit card balances and the different interest rates, and the total amount of money that can be used to pay off the balances, and the site will lay out a payment plan. (Basically, pay off the highest-interest rate balance as much as possible while making minimum required payments on the rest). Most people are surprised at how much can be saved (and how much shorter the time to be debt-free is) if one is willing to pay just a little bit more each month.
The first thing you need to do is look at your terms and conditions of your credit card, or ask your bank, how they will apply the payments. As Dilip notes in his answer, in the US, they will likely apply the minimum payment to the lower rate balance, and then must apply the rest above the minimum to the higher rate balance. In other countries, this will vary by law and custom. Do not assume it will pay off the higher balance, or proportionally, without asking.
Let's take the following example.
You owe $6000. $5000 is at 13.5% (normal purchase rate) and $1000 is at 22% (cash advance rate). If your bank applies payments to both balances proportionally, then a payment of $600 will reduce your purchase balance by $500 and your cash advance balance by $100.
The average APR, then, is simply sum of the product of the APR times balance. So here,
(.135*5000 + .225*1000)/6000 = 15%. This is called a
If the bank applies the payment differently - such as to the lower rate first, or some specified part to the lower rate and the rest to the higher rate - then this will be misleading if you enter it into a calculator, because your average APR will rise over time as you pay off the purchase balance but don't pay off the cash advance balance, or may decrease if the opposite happens.
The weighted average is probably reasonably close in the circumstance that you describe, even if you have rules applying the balance differently, so long as they don't 100% pay down the lower rate - so it may be the simplest option for you in terms of rough calculations (where it's not critical to be correct, just close).
One approach using the online calculators that might be better, is to treat these like two separate loans/cards. Many calculators exist for multiple balances. Then you can allocate funds differently to the two 'cards'. This would allow you to see how long you will need until you've paid off the higher balance, for example, although it probably won't perfectly match things - unless you find a site that has this specific option available you probably will have to either live with a small error in your calculations or do the math by hand.