Suppose you have an investment account with a "Stated Rate" of 7% compounded monthly then the Effective Annual Interest Rate will be about 7.23%. Further, you want to know what your return will be in 5 years. Using the calculator, your periods are years, nominal rate is 7%, compounding is monthly, 12 times per yearly period, and your number of periods is 5.
First calculating the periodic (yearly) effective rate: i = ( 1 + ( r / m ) )m - 1
i = ( 1 + ( 0.07 / 12 ) )12 - 1 = 0.0722901 = 7.22901%
Next calculating the compounded interest rate of i over 5 years: it = (1 + i)t - 1
it = (1 + 0.0722901)5 - 1 = 0.417625 = 41.76%
And we would also get it = ( 1 + ( r / m ) )mt - 1 = 41.76%
Excel function EFFECT()This calculation for effective rate is similar to Excel function EFFECT(nominal_rate,npery) where nominal_rate = r and npery = m.
Continuous CompoundingWhen the frequency of compounding is increased up to infinity we get "continuous compounding". By definition, as n approaches infinity in the term [ ( 1 + ( r / m ) )m ] the value of this term approaches a limit equal to [ er].[1] Where e is the constant [2.7182818284....] and r is the interest rate in decimal form equal to R/100. So,
i = er - 1
I hope this helps!! <3
