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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

    HallsofIvy

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    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

    tiny-tim

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    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.
     
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