# Calculating credit card debt using a geometric series

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1. May 12, 2012

### rosemary1234

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.

2. May 12, 2012

### sjb-2812

Perhaps take it one month at a time. After 1 month, what is the balance before, and after interest?

3. May 16, 2012

### chris_usyd

since apr=18%,then precentage rate is 18%/12=1.5%.
the balance after 1st month=800+800*1.5%
2nd month=(800+800*1.5%-15)(1+1.5%);
3rd month=((800+800*1.5%-15)(1+1.5%)-15))(1+1.5%);
rewirte; 1th month=800*(1+1.5%);
2nd month=800(1+1.5%)^2-15(1+1.5%);
3rd month=800(1+1.5%)^3-15(1+1.5%)^2-15(1+1.5%);
therefore, n month=800*(1+1.5%)^n-15(1+1.55)^(n-1)-15(1+1.5%)^(n-2)...15(1+1.5%)
the part after 800*(1+1.5%)^n is a geometric series///
problem solved !!!