# Nominal Annual Interest Rate

 Effective Annual Interest Rate (r): % Number of Compounding Periods (n): Continuous Compounding? (n is infinity): Yes Nominal Annual Interest Rate (i): %

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 APY 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.