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

  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. phinds

    phinds 9,144
    Gold Member

    Why would the equation for the effective rate be any different than the equation for the nominal rate ?
     
  4. 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. phinds

    phinds 9,144
    Gold Member

    Why would the equation for the effective rate be any different than the equation for the nominal rate ?
     
  6. phinds

    phinds 9,144
    Gold Member

    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.
     
  7. 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]
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?

0
Draft saved Draft deleted