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I Boas 1.13 Compound interest/geometric series

  1. Sep 17, 2016 #1
    From Mary Boas' "Mathematical Methods in the Physical Sciences" Third Edition.

    I'm not taking this class but I was going through the text book and ran into an issue. The problem states:

    If you invest a dollar at "6% interest compounded monthly," it amounts to (1.005)n dollars after n months. If you invest $10 at the beginning of each month for 10 years (120 months), how much will you have at the end of the 10 years?​

    Now, the problem expects you to use the formula for partial sum of a geometric series.
    [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]

    So, as far as I can tell, the series is
    [tex]10*1.005+10*1.005^2+10*1.005^3+...[/tex]
    which would mean:
    a = 10*1.005 = 10.05,
    r = 1.005,
    and n = 120.​

    Computing Sn with those values gives about $1646.99.

    Interestingly, Quora gave the exact same answer: https://www.quora.com/Investing-que...much-will-you-have-at-the-end-of-the-10-years


    My problem? Compound interest calculators give a totally different number. For example:
    http://www.bankrate.com/calculators/savings/compound-savings-calculator-tool.aspx
    gives $2014.
    screencap: https://s15.postimg.org/gxaujjt8b/compoundinterest1.jpg

    https://www.investor.gov/additional...l-planning-tools/compound-interest-calculator
    gives $2013.46.
    screencap: https://s17.postimg.org/4ai0gb7xb/compoundinterest2.jpg




    So, I am kind of lost here. Did I do the problem wrong? If so please enlighten me. I double checked their value of 1.005 using (1+r/n)nt; (1 + 0.06/12) = 1.005, so 1.005n appears to be valid to me.


    Any suggestions?
     
  2. jcsd
  3. Sep 17, 2016 #2

    Bystander

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    Think about the differences among annual/yearly, monthly (which you've got), and "continuous" compounding.
     
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