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Is there any way to derive an equation for compound interest based

  1. Feb 18, 2014 #1
    Is there any way to derive an equation for compound interest based on effective interest rate instead of the nominal interest rate?
     
  2. jcsd
  3. Feb 18, 2014 #2

    phinds

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    Why would the equation for the effective rate be any different than the equation for the nominal rate ?
     
  4. Feb 18, 2014 #3
    I am aware of this equation for compound interest based on nominal interest:

    $$F=P{ e }^{ rt }\\ where\quad r=nominal\quad annual\quad interest\\ and\quad t=number\quad of\quad years$$

    How would I modify it for effective interest?
     
  5. Feb 18, 2014 #4

    phinds

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    Why would the equation for the effective rate be any different than the equation for the nominal rate ?
     
  6. Feb 18, 2014 #5
  7. Feb 18, 2014 #6

    phinds

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    That's interesting. I was interpreting "effective" in this context to mean "real", which is not at all what it means. Basically the "effective" rate is just the nominal rate plus a very small amount, it has nothing to do with the real rate.
     
  8. Feb 18, 2014 #7

    Chestermiller

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    This equation assumes that there is continuous compounding at the nominal interest rate. The relationship between the nominal interest rate in this equation and the effective interest rate I is found by calculating the principal after 1 year:

    [tex]Pe^r=P(1+I)[/tex]
    So, [tex]I=e^r-1[/tex]

    If we substitute this into your original equation, we obtain:
    [tex]F=(1+I)^t[/tex]
    More generally, if there are n compounding periods a year, and r is the nominal interest rate,

    [tex]F=P(1+\frac{r}{n})^{nt}[/tex]
    So, [tex](1+\frac{r}{n})^{n}=(1+I)[/tex]
    So,[tex]I=(1+\frac{r}{n})^{n}-1[/tex]
     
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