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Financial Mathematics - Annuities

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  1. Jul 29, 2009 #1
    http://www.intmath.com/Money-Math/annuity_6.gif [Broken]

    Above is the annuities formula (change the - to a + as i am not using it for loans) used to calculate the amount of money accumulated over a period of time with compounding interest, with a monthly input of $W.

    the first part is an example of a Geometric Sequence i believe.
    P(1+r)^n

    I would like to find out how this formula would be altered if my input (W) was becoming greater by approx 3% p.a ?

    any help is greatly appreciated!!

    Thanks heaps!

    ~James Radford-Voss
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 29, 2009 #2

    Mentallic

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    I haven't had the benefit of studying annuities or even using this or similar formulas for that fact, so I don't know precisely what the formula represents.

    However, I'll throw in an idea to see if it helps.

    Since your $W is increasing by 3%/annum, couldn't we use another geometric sequence to express this?
    So maybe (emphasis on the maybe), the W should be substituted with, say:

    [tex]W(1+\frac{A}{100})^{m}[/tex]

    where A is the increase in percentage (3 in this case)
    m is the frequency of increase (per annum, hence, 1 in this case)

    This is just a guess, so don't take my word for it, and be very skeptical when attempting to consider its legitimacy :smile:
     
  4. Jul 29, 2009 #3

    HallsofIvy

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    Then you would replace W by 1.03W so your formula becomes
    [tex]B= P(1+ r)^n+ 1.03W\frac{(1+r)^n-1}{r}[/tex]
    [tex]= P(1+ r)^n+ W\frac{(1+r)^n-1}{r}+ 0.03W\frac{(1+r)^n-1}{r}[/tex]

    and the increase is that
    [tex]0.03W\frac{(1+r)^n-1}{r}[/tex].
     
    Last edited by a moderator: May 4, 2017
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