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Interest problem

  1. Apr 20, 2009 #1
    1. The problem statement, all variables and given/known data
    This is not a problem in my calculus book.However, I am sure this involves calculus. This is also not a question from an economics class, it is just curiosity.

    My question is: If I have a debt that is continually compounded, and I continually pay off the debt at a constant rate, how long will it take to pay off the debt?


    2. Relevant equations
    Compund interest(PERT)


    3. The attempt at a solution
    Let:
    r=rate on the debt. (assume annually)
    y= amount of money I will pay per year.
    [tex]\Delta[/tex]t= an increment of time of which I will pay a quanta of money.

    During the time [tex]\Delta[/tex] t since I started the debt, I will owe er[tex]\Delta[/tex]t

    At this point I will pay my first quanta of money which would be y[tex]\Deltat[/tex]. and w

    Right before I make my second payment on time 2[tex]\Delta[/tex]t, I will owe the money f
    money owed from last increment AND the compound interest since that time.
    ie I will owe (et[tex]\Delta[/tex]t-y[tex]\Delta[/tex]t)er[tex]\Delta[/tex]t=e2r[tex]\Delta[/tex]t-y[tex]\Delta[/tex]te[tex]\Delta[/tex]t

    Continuing the pattern, the money I would owe right before my nth payment is:

    en[tex]\Delta[/tex]t-y[tex]\Delta[/tex]te(n-1)[tex]\Delta[/tex]t


    This is getting a bit tough. Where do I go from here?
     
    Last edited: Apr 20, 2009
  2. jcsd
  3. Apr 20, 2009 #2
    Latex isn't working right now. It's bit hard to read.

    But are you referring to a cash flow problem (annuities) i.e. there is a negative cash flow at t =0, and at the end of each year/month, there are equal positive cash flows.
    http://www.zenwealth.com/BusinessFinanceOnline/TVM/Annuities.html


    (it doesn't consider inflation)
     
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