# Annual Percentage Yield

﻿
Annual Percentage Yield

Annual Percentage Yield (APY) expresses an annual rate of interest taking into account the effect of compounding, usually for deposit or investment products (such as a certificate of deposit). It is analogous to the Annual percentage rate (APR), which is used for loans. 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.

:$APY = left\left(1 + frac \left\{i_\left\{nom \left\{N\right\} ight\right)^N -1$

where :$i_\left\{nom\right\}$ is the nominal interest rate and:$N$ is the number of compounding periods per year.

For large "N" we have, approximately,

:$APY approx e^\left\{i_\left\{nom - 1,$

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 also Annual 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. For financial institutions in the United States, the calculation of the APY and the related Annual Percentage Yield Earned (APYE) are regulated by the FDIC Truth in Savings Act (TISA) of 1991.

References

* [http://www.fdic.gov/regulations/laws/rules/6500-3400.html FDIC Law, Regulations, and Related Acts] - text of the Truth 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).

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

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• annual percentage yield — ( APY) A precisely calculated measure of yield paid on a bank deposit account. American Banker Glossary ( APY) The effective, or true annual rate of return. The APY is the rate actually earned or paid in one year, taking into account the effect… …   Financial and business terms

• annual percentage yield — /ˌænjuəl pəˌsentɪdʒ ji:ld/ noun the annual rate of compound interest earned by an account. Abbreviation APY …   Dictionary of banking and finance

• Annual Percentage Yield - APY — The effective annual rate of return taking into account the effect of compounding interest. APY is calculated by: The resultant percentage number assumes that funds will remain in the investment vehicle for a full 365 days. The APY is similar in… …   Investment dictionary

• Annual percentage yield (APY) — The effective, or true, annual rate of return. The APY is the rate actually earned or paid in one year, taking into account the affect of compounding. The APY is calculated by taking one plus the periodic rate and raising it to the number of… …   Financial and business terms

• annual effective yield — See: annual percentage yield. Bloomberg Financial Dictionary …   Financial and business terms

• Annual percentage rate — Parts of total cost and effective APR for a 12 month, 5% monthly interest, \$100 loan paid off in equally sized monthly payments. The term annual percentage rate (APR), also called nominal APR, and the term effective APR, also called EAR,… …   Wikipedia

• Annual Percentage Rate - APR — The annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number that represents the actual yearly cost of funds over the term of a loan. This includes any fees or additional costs associated with the… …   Investment dictionary

• yield to call — ( YTC) The annual percentage yield of a security calculated using the yield to maturity formula but with the assumption that the security is called on the first call date or on the first par call date. American Banker Glossary The percentage rate …   Financial and business terms

• yield-to-maturity — ( YTM) The annual percentage yield of a security calculated in a specific manner. The yield to maturity is the single discount rate that, when applied to all future interest and principal payments, produces a net present value equal to the… …   Financial and business terms

• annual rate of return — There are many ways of calculating the annual rate of return. If the rate of return is calculated on a monthly basis, we sometimes multiply this by 12 to express an annual rate of return. This is often called the annual percentage rate ( APR).… …   Financial and business terms