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The number e

  1. May 9, 2012 #1
    I'm trying to figure out what the number e is all about.

    100 * .1 = 110
    110 * .1 = 121
    110 * .1 = 133.1

    that should be equal to 100e.4, right?

    well, 100e.4 = 134.99, not 133.1

    What am I doing wrong?
     
  2. jcsd
  3. May 9, 2012 #2

    Dick

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    I have no idea what you are doing, right or wrong. 100*.1=10. Can you explain?
     
  4. May 9, 2012 #3
    the formula for calculating continuous compound interest is

    A = Pert

    Where A = final amount
    P = initial amount
    r = rate
    t = time

    if you start with 100 dollars and the rate is 10% after 3 payment periods it should be 134.99 based on the above formula.

    well, 100 * 1.1 is 110, 110 * 1.1 = 121, 121 * 1.1 = 133.1, not 134.99
     
  5. May 9, 2012 #4

    Dick

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    Your formula is only valid for continuously compounded interest. Not for interest paid at intervals.
     
  6. May 9, 2012 #5
    ok, thanks, i thought they were the same but i was wrong.
     
  7. May 10, 2012 #6
    e is what happens when you continuously compound something over an infinitely short interval.
    [itex]x\stackrel{lim}{\rightarrow}∞[/itex] (1+[itex]\frac{1}{x}[/itex])x=e
     
  8. May 10, 2012 #7

    Ray Vickson

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    They can be made to give the same results at integer values of time t = 1,2,3,..., but you need to adjust the rate. In order to have a continuous interest rate r give a true annual interest of i you need to have
    [tex] e^r = 1 + i, \text{ or } r = \ln(1+i).[/tex]

    In your example, to get a true annual interest rate of 10% you need to take a continuous interest rate of 9.531017980%, giving r = 0.0953101798. If you take, instead, a continuous rate of 10% you get a true annual rate of [itex] i = e^{0.1}-1 = 0.105170918,[/itex] or about 10.5171%. This is the origin of the differences you note.

    RGV
     
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