# Credit Card minimum payment

• Jun 12th 2009, 07:35 PM
ibrox
Credit Card minimum payment
Your Visa card says its annual interest rate is 18%. Of course, you are asked to make monthly payments. If you have a balance of \$1,000, how long would it take you to pay off the balance assuming you make the minimum payment of 3.0% a month?

I understand its the reverse of a bank account where you make constant deposits and the interest accumulates, but I am having a tough time with this. Thanks.
• Jun 12th 2009, 07:58 PM
aidan
Quote:

Originally Posted by ibrox
Your Visa card says its annual interest rate is 18%. Of course, you are asked to make monthly payments. If you have a balance of \$1,000, how long would it take you to pay off the balance assuming you make the minimum payment of 3.0% a month?

I understand its the reverse of a bank account where you make constant deposits and the interest accumulates, but I am having a tough time with this. Thanks.

At some point you'll need to make an absolute minimum payment of an unchanging amount.
Otherwise the postage will cost more than the minimum 3% payment to be made, for a long time.
Without a set-or-fixed minimum \$ amount at some point the exercise is not useful.

It would be more meaningful to say that the minimum payment is 3% or \$5 (or \$10), which ever is greater. Then you have a believable predicament.
• Jun 13th 2009, 03:10 PM
ibrox
Ok. I got confirmation standard rules apply.

IE. Minimum payment is \$10 or 3%, whichever is greater.
• Jun 14th 2009, 04:05 AM
HallsofIvy
18% annual interest is 18/12= 3/2= 1.5% monthly interest.To start with, ignore that \$10 minimum. Suppose at some month the amount left to pay off is A. Then you would make the minimum payment of 0.03A and the interest for that month, 0.015A, wold be subtracted leaving an actual payment on the principal of (0.03- 0.015)A= 0.015A. Subtracting that payment from the principal leaves (1- 0.015)A= 0.985A still to be payed off.

That is, each month, the principal amount will be multiplied by 0.985. After n months, the initial amount will have been multiplied by $(0.985)^n$ and the account will have been payed off when $(0.985)^nA= 0$. Of course, that's impossible! That would be the same a saying $(0.985)^n= 0$ and an exponential is never 0. That was aidan's point and why that \$10 minumum is required.

The 3% payment will drop below \$10 when 0.03A= 10 or A= 10/0.03= \$333.33. So use the above calculation until $(0.985)^nA\le 333.33$, then see how many \$10 paymeants are required to finish the payoff.
• Jun 14th 2009, 05:19 PM
ibrox
I understand your line of thinking, but upon doing the question, I discovered something different. Even though you are paying 18% a month, you are really paying 19.56% a year. Becuase it is a Visa credit card bill and that you are to pay monthly, you are correct in that you pay 1.5% a month in interest. Consider this, you have a balance of \$1 on your bill. Assuming no payments are made for an entire year, you get:

\$1 x 1.015^12 = \$1.195618

So, in reality, we are paying an effective interest rate of 19.56% a year. Makes it confusing what do I go with I guess lol. But Id use the same formula given right?
• Jun 16th 2009, 08:22 PM
TKHunny
In the US, you may have an additional floor:

1% + Actual Charges in the Billing Period