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The concept of both is the same thing – calculating the annualized return rate of a security.

Effective annual yield (EAY) usually calculates the annualized holding period yield (HPY) or yield to maturity (YTM), which is the return earned when a security is held until maturity. Remember that EAY:

- (Usually) assumes 365 days in a year
- Incorporates compounding

Formula:

$EAY={\left(1+HPY\right)}^{\frac{365}{t}}\u20131$

where HPY = holding period yield (or YTM)

Effective annualized rate (EAR) is usually converting a % rate (e.g. nominal 8% paid quarterly) to a rate that indicates the actual interest paid when compounding is taken into account. EAR tends to ‘scale up’ or ‘scale down’ payment periods such as semi-annually, quarterly, etc.

So for a nominal 8% rate paid quarterly:

Formula:

$EAR={\left(1\u2013\frac{annualnominalrate}{\#paymentsayear}\right)}^{\#paymentsayear}\phantom{\rule{0ex}{0ex}}={\left(1\u2013\frac{0.08}{4}\right)}^{4}\phantom{\rule{0ex}{0ex}}=8.24\%$