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Tells you nominal annual interest rate, given the effective annual interest rate and the number of compounding periods.
Nominal Annual Interest Rate Formulas:
If the Effective Interest Rate or APR is 8.25% compounded monthly then the Nominal Annual Interest Rate or "Stated Rate" will be about 7.95%. An effective interest rate of 8.25% is the result of monthly compounded rate x such that i = x * 12.
The formula can be written as:
i = n * ( [ (1+r)^(1/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". Using our formula from our Effective Annual Interest Rate Calculator, where r = e^i - 1 becomes e^i = r + 1. And, by definition ln(e^i) = i [1], we can solve for i to get the formula:
i = ln(r + 1).
References
[1] Algebra and Trigonometry: A Functions Approach; M. L. Keedy and Marvin L. Bittinger; Addison Wesley Publishing Company; 1982.
Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, 2003.
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