# Thread: calculating credit card debt using a geometric series

1. ## calculating credit card debt using a geometric series

A man gets a credit card and buys something that charges exactly 800 dollars to the card. The APR on the card is 18 % compounded monthly, and the minimum payment is 15 dollars a month. What is the expression for A(n), the balance on the card after n months? (This should be a geometric series).

I have tried to come up with different formulas, and none provide answers that make sense. I have tried to fit the information into formulas combining the sum of a geometric series and compound interest, with no luck.

A man buys 800 dollars worth of stuff on his new credit card. There is 18% APR compounded monthly. What is the smallest monthly payment he could have to pay off the debt in a finite amount of time.
I've tried to apply the formula for the sum of an infinite geometric series, but it is not making sense or helping. That is the only thing i've worked with that has dealt with the concept of infinite, so i'm a little confused. Any suggestions on how to approach this?

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2. ## Re: calculating credit card debt using a geometric series

try this:
800 dollars accumulated for n months
- 15 accumulated for n-1 months
- 15 accumulated for n-2 months
- 15 accumulated for n-3 months
.....

The terms involving "15" will be ageometric series.

3. ## Re: calculating credit card debt using a geometric series

Thanks! i think i have a equation: A(n)=(785(1-.18/12)^n-(15(1+.18/12)^n/1+.18/12

4. ## Re: calculating credit card debt using a geometric series

Huh?
$800 @ 18% for 1 month = 800 * .18/12 =$12 interest.
So to pay off in a FINITE number of months, needs to pay 12.01 monthly:
that's take 477 months...39 3/4 years !

5. ## Re: calculating credit card debt using a geometric series

Thanks Wilmer! I think i understand the problem now