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Geometric sequences

  1. Jun 1, 2008 #1
    1. The problem statement, all variables and given/known data
    A mortgage is taken out for £80,000. It is to be paid by annual instalments of 5000with the first payment being made at the end of the first year that the mortgage was taken out. Interest of 4% is then charged on any outstanding debt. Find the total time taken to pay off the mortgage.


    2. Relevant equations
    Sn=a(r^n-1)/r-1


    3. The attempt at a solution

    I have no idea here can someone please point me in the right direction, thanks!
     
  2. jcsd
  3. Jun 1, 2008 #2
    Since you want a pointer in the right direction, start with your 80K subtract the payment 5K...then add to what remains 4% interest, then subtract 5K again and add to what remains 4% interest, then subtract...and so on. (so long as you don't actually calculate anything here you should see that you'll be summing up terms in a geometric sequence)
    Clearly if you keep repeating this process the debt will become zero. the n in your relevant equation is the number of times interest gets added.
    For what value of n will it be true that your above summation will be equal to zero?
     
    Last edited: Jun 1, 2008
  4. Jun 1, 2008 #3
  5. Jun 1, 2008 #4
    I'm getting just over 12 years, is that correct?
     
  6. Jun 1, 2008 #5
    it dosen't sound right
     
  7. Jun 1, 2008 #6
    with no interest, paying 5000/year. it would take 80000/5000 = 16 years to pay it off. it's going to be more than that with interest
     
  8. Jun 1, 2008 #7
    what expression did you form to get that?
    furthermore, shouldn't your sum equation be of the form: Sn = (r^(n+1)-1)/(r-1)?

    Hmm..am I right in saying that you got 12 years by the following process:
    1.a): 80000-5000
    1.b): (1.a) - 0.04*(1.a)
    1.c): (1.b) - 5000
    1.d): (1.c) - 0.04*(1.c)...and so on?
     
    Last edited: Jun 1, 2008
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