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Is there any way to derive an equation for compound interest based... 
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#1
Feb1814, 10:39 AM

P: 154

Is there any way to derive an equation for compound interest based on effective interest rate instead of the nominal interest rate?



#2
Feb1814, 10:42 AM

PF Gold
P: 6,276

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



#3
Feb1814, 10:45 AM

P: 154

$$F=P{ e }^{ rt }\\ where\quad r=nominal\quad annual\quad interest\\ and\quad t=number\quad of\quad years$$ How would I modify it for effective interest? 


#4
Feb1814, 12:35 PM

PF Gold
P: 6,276

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



#5
Feb1814, 05:07 PM

P: 542

See if this helps...
Difference Between Nominal & Effective Interest Rates http://www.ehow.com/info_8149388_dif...estrates.html 


#6
Feb1814, 06:28 PM

PF Gold
P: 6,276




#7
Feb1814, 07:35 PM

Sci Advisor
HW Helper
Thanks
PF Gold
P: 5,177

[tex]Pe^r=P(1+I)[/tex] So, [tex]I=e^r1[/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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