# Annual Percentage Yield - Equation

Equation

One common mathematical definition of APY uses this effective interest rate formula, but the precise usage may depend on local laws.

where

is the nominal interest rate and
is the number of compounding periods per year.

For large N we have, approximately,

where e is the base of natural logarithms (the formula follows the definition of e as a limit). This is a reasonable approximation if the compounding is daily. Also, it is worth noting that a nominal interest rate and its corresponding APY are very nearly equal when they are small. For example (fixing some large N), a nominal interest rate of 100% would have an APY of approximately 171%, whereas 5% corresponds to 5.12%, and 1% corresponds to 1.005%.

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### Famous quotes containing the word equation:

A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.
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