Effective Annual Interest Rate

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Tells you effective annual interest rate, given the nominal annual interest rate and the number of compounding periods. If you have a loan with a nominal interest rate of 7% per year and you will be making monthly payments, enter 7% and 12. If you are making quarterly payments, enter 7% and 4.

Effective Annual Interest Rate Formulas:

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.

Continuous Compounding

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]

References

[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.