PS2

PAYING OFF CREDIT CARD DEBT

Each month, a credit card statement will come with the option for you to pay a minimum amount of your charge, usually 2% of the balance due. However, the credit card company earns money by charging interest on the balance that you don't pay. So even if you pay credit card payments on time, interest is still accruing on the outstanding balance.

Say you've made a $5,000 purchase on a credit card with an 18% annual interest rate and a 2% minimum monthly payment rate. If you only pay the minimum monthly amount for a year, how much is the remaining balance?

You can think about this in the following way.

At the beginning of month 0 (when the credit card statement arrives), assume you owe an amount we will call b0.

Any payment you make during that month is deducted from the balance. Let's call the payment you make in month 0, p0. At the beginning of month 1, the credit card company will charge you interest on your new balance. So if your annual interest rate is r, then at the beginning of month 1, your new balance is your previous balance b0 less the payment p0 plus interest on this new balance for the month. In algebra, this new balance would be

b1=(b0−p0)⋅(1+r12)

In month 1, we will make another payment, p1. That payment has to cover some of the interest costs, so it does not completely go towards paying off the original charge, and thus at the beginning of month 2, our balance would be

b2=(b1−p1)⋅(1+r12)

If you choose just to pay off the minimum monthly payment each month, you will see that the compound interest will dramatically reduce your ability to lower your debt.

For example, if the minimum monthly payment is 2% of the current balance, we would have

Month	 Balance	 Payment	 Interest
0	 5000.00	 100 (= 5000 * 0.02)	 73.50 (= (5000 - 100) * 0.18/12)
1	 4973.50 (= 5000 - 100 + 73.50)	 99.47 (= 4973.50 * 0.02)	 73.11 (= (4973.50 - 99.47) * 0.18/12)

You can see that a lot of your payment is going to cover interest, and if you work this through, you will see that after a year, you will have paid $1259.45 and yet you will still owe $4691.11 on what was originally a $5000.00 debt. Pretty depressing!