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Best Strategy for Paying Off Credit Card Debt

Date: 04/30/2007 at 23:53:35
From: Gavin
Subject: Credit card payment - optimize payment schedule

I am trying to find out what formula I can use to determine my most
optimal payment schedule (one that provides the lowest amount of 
interest paid) under a given budget.  I have 5 accounts, each with
different APRs and different account balances.  Also, two of the 
accounts have a zero percent interest rate for "x" number of months
but will resume their standard APR at the end of the "x" month time

The reason I was thinking that this might not be possible (or a highly
complicated calculation) is because I seem to think that each credit
card would have to be calculated separately.  Thanks for the help.

Date: 05/01/2007 at 20:06:20
From: Doctor Vogler
Subject: Re: Credit card payment - optimize payment schedule

Hi Gavin,

Thanks for writing to Dr. Math.

Except possibly in cases of changing interest rates, you always want
to make the largest payment possible to the highest-rate loan.  So you
should make minimum payments on lower-rate cards and pay as much as
you can afford on the highest-rate cards until they are paid off. 
Each time one card is paid off, start making the highest payments you
can afford on the next-highest-rate card.

By that rule, the zero-interest cards would always be paid off last. 
This is usually the best thing to do anyway, unless the pay-off is
going to take a long time, AND the new rate after the 0% wears off is
significantly higher than other cards that you are paying off.  In
that case, it might be advantageous to start working away at the 0%
before it jumps to a higher rate.

There is one other wrinkle in this:  Often a single card can have
various charges on it that accrue interest at different rates.  All
credit cards I've seen say that your payment goes toward lower-rate
balances first (which is most beneficial to them, least beneficial to
you).  That means that you can't always get at the highest rate,
because you might have a different balance on the same card with a
lower rate.  As with the expiring 0%, whether it is better to work on
paying off a lower rate in order to expose the higher rate on the same
card, or just working on other cards first, depends on how long the
pay-off is going to take, and how much higher the higher rate is than
other cards.

For the same reason, if you have a low-interest balance on a card
(such as a 0% balance transfer), then you should always avoid using
the same card for higher-rate charges, because then you'll be forced
to pay interest on the higher-rate charges until you pay off the
lower-rate balance (whereas you want to do it in the other order).

If you have any questions about this or need more help, please write
back and show me what you have been able to do, and I will try to
offer further suggestions.

- Doctor Vogler, The Math Forum 

Date: 05/01/2007 at 21:34:39
From: Gavin
Subject: Credit card payment - optimize payment schedule

Thank you for your time and your response.  

I understand the basic logic that you have provided me, however I
still feel like there is something that needs to be addressed.  You
commented that it is usually best to pay off the card with the highest
interest rate first, then to pay off the next highest, etc..  However, 
if I am not mistaken that is not necessarily the case.  Please 
consider this situation:

"I owe $4,500 at a 15% interest rate and $20,000 at a 13% interest
rate.  Also, I only have a budget of $1,000 each month to put toward
my credit card payments."

If your method of repayment is applied I would focus on the $4,500
balance first only paying the minimum monthly payment on the $20,000
balance until the $4,500 balance is paid off.  Then, I would focus all
of my budget on the $20,000 balance since it is the only one 

Now, I may be mistaken (or these just might not be the right numbers
to demonstrate my point) but in a situation similar to this, one in
which you have a relatively low balance with a higher interest rate
and a relatively high balance with a lower interest rate, it seems
that your method of repayment would in fact accrue more interest than
if you where to put a bigger dent early on into the higher balance.  
It seems that in relative terms, even though the interest rate is
lower on the $20,000 balance, you would in fact pay more interest on
it simply because the balance is so high.

For example, if the minimum monthly payment was 2.5 percent of the
balance, that would be a $500 payment to the $20,000 account.  That
only leaves $500 to go toward the $4,500 account and of course $56.25
of that $500 goes toward interest.

Like I said, the numbers I used might not prove my point (and maybe
I'm flat out mistaken), but it seems that there should be a formula
that I can derive that will allow me to calculate the proper payment
schedule for the situation that I originally described (one with 5
accounts, all with different balances, different APRs, different
required monthly payments, and a restrained budget).

Once again, thank you for your time and response. 

Date: 05/03/2007 at 16:53:21
From: Doctor Vogler
Subject: Re: Credit card payment - optimize payment schedule

Hi Gavin,

The amount that goes to interest in each card this month cannot be 
changed.  The question is how your payment this month affects the 
interest next month.  See what happens to the total interest paid 
next month in each scenario:

  (1) this month, you pay the minimum $500 to the $20,000 balance at
13% and the remaining $500 to the $4,500 balance at 15%

  (2) this month, you pay the minimum $113 to the $4,500 balance at
15% and the remaining $887 to the $20,000 balance at 13%

I think you'll find that you'll pay less interest next month if you 
pay as much as you can toward the 15% balance and only the minimum 
toward the 13% balance.

So I stand by what I said the last time.

- Doctor Vogler, The Math Forum 
Associated Topics:
High School Interest

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