# What the heck?

What the heck???

The minimum monthly payment for a credit card is the larger of $5 or 1/25 of the outstanding balance. If the balance is less than$5, then the entire balance is due. If you make only the minimum payment each month, how long will it take to pay off a balance of $200? Clearly, this has to do with geometric series. I can conceptually understand this problem, but I'm having trouble putting it into mathematical terms while relating to geometric series. If you have any advice, I would greatly appreciate it. Thanks. ## Answers and Replies Related Precalculus Mathematics Homework Help News on Phys.org HallsofIvy Science Advisor Homework Helper First, when do you start making a minimum payment of$5? x/25= 5 when x= 125 so how many payments will be required to bring the balance down to $125? If your initial balance is S and you pay a fraction r of that each month, you first payment will be rS and the remaining balance S- rS= S(1-r). Your second payment will be r(1-r)S and the remaining balance then will be S(1-r)- r(1-r)S= (1-r)(S- rS)= (1-r)2S. The remaining balance, after n payments, is the geometric sequence (1-r)nS. For what n is (1- 1/25)n(200)< 125? At that point the balance will be between 120 and 125 and will require 120/5= 22 payments of$5 each and a final payment of less than \$5.

tiny-tim
Homework Helper
What the heck???
oh … I have never seen such language! :surprised

Tush! And pish!
Clearly, this has to do with geometric series. I can conceptually understand this problem, but I'm having trouble putting it into mathematical terms while relating to geometric series. If you have any advice, I would greatly appreciate it. Thanks.
Hi Calixto! Geometric sequence, actually.

Choose a name, like Pn, for the amount of money remaining after n months, and then find the formula connecting Pn and Pn-1. 