(: calculate the effective annual interest rate if the annual interest rate, i, is 8%. i=(1+r12)12−1 a.0.7990 b. 0.083 c. 0.0855 d. 0.0900

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%

This calculation for effective rate is similar to Excel function EFFECT(nominal_rate,npery) where nominal_rate = r and npery = m.

When 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

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