1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: What the heck?

  1. Jun 5, 2008 #1
    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.
  2. jcsd
  3. Jun 5, 2008 #2


    User Avatar
    Science Advisor

    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.
  4. Jun 5, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    oh … I have never seen such language! :surprised

    Tush! And pish!
    Hi Calixto! :smile:

    Geometric sequence, actually.

    General advice:

    Be systematic.

    Choose a name, like Pn, for the amount of money remaining after n months, and then find the formula connecting Pn and Pn-1. :smile:
  5. Jun 5, 2008 #4
    Ok thanks HallsOfIvy, that helps a lot. And sorry tiny-tim for using such offensive language.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook