Retrieving "Effective Annual Yield" from the archives

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1. Annual Percentage Yield

   Linked via "effective annual yield"

   Calculation and Theoretical Basis
   The mathematical foundation of APY rests upon the formula for future value under discrete compounding. If $r$ is the nominal annual interest rate (expressed as a decimal) and $n$ is the number of compounding periods per year, the APY is derived from the effective annual yield ($r_{eff}$).
   The relationship is defined by the following equation:

2. Effective Yield

   Linked via "effective annual yield"

   Calculation and Definition
   The fundamental distinction between nominal interest rate and effective yield ($r{eff}$) arises when interest is not compounded only once per period. If compounding occurs $n$ times per year, the effective annual yield} is calculated using the formula:
   $$ r{eff} = \left(1 + \frac{r{nom}}{n}\right)^n - 1 $$

3. Effective Yield

   Linked via "effective annual yield"

   APR (Annual Percentage Rate}): Generally reflects the nominal rate} ($r_{nom}$) divided by the number of compounding periods per year, often ignoring any actual compounding effect, thus understating the true cost of borrowing} in many jurisdictions [7].
   APY (Annual Percentage Yield}): Is functionally equivalent to the effective annual yield} ($r_{eff}$) assuming compounding occurs over a full year. However, [regulatory st…