Tells you effective annual interest rate, or APY (annual percentage yield), given the nominal annual interest rate and the number of compounding periods. If you have an investment earning a nominal interest rate of 7% per year and you will be getting interest compounded monthly, enter 7% and 12. If you are getting interest compounded quarterly on your investment, enter 7% and 4.
If the Nominal Interest Rate (also known as the "Stated Rate") is stated as 7% compounded monthly then the Effective Annual Interest Rate will be about 7.22%. A nominal interest rate of 7% will become 7%/12 months = 0.583% per month (0.07/12 months = 0.00583 per month). Compounding monthly (1 + 0.00583)^12 = 1.0722 which becomes 1.0722 - 1 = 0.0722 = 7.22%.
The formula can be written as:
r = [ (1+i/n)^n ] - 1,
where r is the effective rate, i is the stated rate and n is the number of compounding periods.
This calculation is equivilant to the Excel function EFFECT(nominal_rate,npery) where nominal_rate = i and npery = n.
When the frequency of compounding is increased up to infinity we get "continuous compounding". By definition, as n approaches infinity in the term [ (1+i/n)^n ] the value of this term approaches a limit equal to [e^i ].[2] Where e is the constant [2.7182818284....] and i is the interest rate in decimal form. So,
r = e^i - 1.[1]
[1] http://www.answers.com/topic/effective-interest-rate-1
[2] Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, 2003.
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