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Interest and Investments

  1. Nov 5, 2007 #1
    Problem:
    What is the final difference in account values if $100,000 is invested in a) a project with returns of 7% / yr or b) one with returns of 5% / yr. Let the period of investment be 40 years.
    This problem is quite simple in theory, and I know the answer should be 100,000(1.07^40 - 1.05^40) = $793446.91. However, this problem is for a logic class in which we are not permitted to use calculators.

    Using a couple Taylor expansion approximations -- for the range of values in question, (1+x)^n = e^(nx) -- I get the following:
    1.07^40 = e^2.8 and 1.05^40 = e^2.
    Basically, all I need to know is how to simplify the expression e^2.8 - e^2 , and then I can simply multiply by $100k to get an accurate approximation.
     
  2. jcsd
  3. Nov 5, 2007 #2
    anyone? :/
     
  4. Nov 5, 2007 #3

    Astronuc

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    Staff: Mentor

  5. Nov 5, 2007 #4
    yeah, the binomial expansion was my first thought, but because nx (40 * 0.02) is not <<1 in this case, I would have to take out the series to a large and undetermined number of terms to produce an answer that is even remotely within the ball park.
     
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