- Annual Percentage Yield
**Annual Percentage Yield**(**APY**) expresses an annual rate ofinterest taking into account the effect of compounding, usually for deposit or investment products (such as acertificate of deposit ). It is analogous to theAnnual percentage rate (APR), which is used forloan s. In some jurisdictions, the use and definition of annual percentage yield may be regulated by a government agency, in which case it would generally be capitalized.The annual percentage yield is generally used to refer to the rate paid to a depositor or lender by a financial institution, whereas

annual percentage rate refers to the rate paid to a financial institution by a borrower. Since the yield is to the lender, however, perspective may lead to confusion about the term: for example, a banker (as lender) may refer to the yield on the bank's loan portfolio, whereas borrowers would refer to the interest rate on their loans from the bank. Similarly, borrowers from a bank may refer to the yield on their deposits, while the bank refers to the rate paid on their deposit accounts.**Equation**One common mathematical definition of APY uses the

effective interest rate formula, but the precise usage may depend on local laws.:$APY\; =\; left(1\; +\; frac\; \{i\_\{nom\; \{N\}\; ight)^N\; -1$

where :$i\_\{nom\}$ is the

nominal interest rate and:$N$ is the number of compounding periods per year.For large "N" we have, approximately,

:$APY\; approx\; e^\{i\_\{nom\; -\; 1,$

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 161%, whereas 5% corresponds to 5.12%, and 1% corresponds to 1.005%.

The

**Annual Percentage Yield**does not take transaction costs on loans or savings accounts into account, see alsoAnnual percentage rate . To promote financial products, banks and other firms will often quote the APY (as opposed to the APR because the APY represents the customer receiving a higher return at the end of the term). Disclosure of the APY is intended to help consumers easily compare products that are offered at different nominal rates and different compounding schedules. Forfinancial institution s in theUnited States , the calculation of the APY and the related**Annual Percentage Yield Earned**(APYE) are regulated by the FDICTruth in Savings Act (TISA) of1991 .**References*** [

*http://www.fdic.gov/regulations/laws/rules/6500-3400.html FDIC Law, Regulations, and Related Acts*] - text of theTruth in Savings Act

* [*http://www.fdic.gov/regulations/laws/rules/6500-3270.html#6500appendixatopart230 Appendix A to Part 230 of TISA*] (specifically covers calculation of APY).**External links*** [

*http://www.numericalexample.com/content/view/27/27 APY calculator*] .

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