Annual percentage yield
Barron's Banking Dictionary:
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Annual Percentage Yield (APY)
Amount of interest expressed as a percentage rate, a deposit account (or a share draft account) would earn in a year at a stated interest rate. The APY disclosure, showing the effect of interest compounding, assumes that funds remain on deposit for a full 365-day year at the advertised rate, and no additional deposits or withdrawals are made. See also Truth in Savings.
Investopedia Financial Dictionary:
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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.
Investopedia Says:
The APY is similar in nature to the annual percentage rate. Its usefulness lies in its ability to standardize varying interest-rate agreements into an annualized percentage number.
For example, suppose you are considering whether to invest in a one-year zero-coupon bond that pays 6% upon maturity or a high-yield money market account that pays 0.5% per month with monthly compounding.
At first glance, the yields appear equal because 12 months multiplied by 0.5% equals 6%. However, when the effects of compounding are included by calculating the APY, we find that the second investment actually yields 6.17%, as 1.005^12-1 = 0.0617.
Related Links:
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Banks use these rates to entice borrowers and investors. Find out what you're really getting. APR and APY: Why Your Bank Hopes You Can't Tell The Difference
Wikipedia on Answers.com:
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Annual percentage yield
"APY" redirects here. For the Australian Aboriginal area, see Anangu Pitjantjatjara Yankunytjatjara.
Annual percentage yield (APY) (also called Effective Annual Rate (EAR) in finance) is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow for a reasonable, single-point comparison of different offerings with varying compounding schedules. However, it does not account for the possibility of account fees affecting the net gain. APY generally refers to the rate paid to a depositor by a financial institution, while the analogous annual percentage rate (APR) refers to the rate paid to a financial institution by a borrower.
To promote financial products that do not involve debt, 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). For example, a CD that has a 4.65 percent APR, compounded monthly, for 8-months would instead be quoted as a 4.75 percent APY [1].
Equation
One common[citation needed] mathematical definition of APY uses the 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%.
United States
For financial institutions in the United States, the calculation of the APY and the related annual percentage yield earned are regulated by the FDIC Truth in Savings Act of 1991:
ANNUAL PERCENTAGE YIELD.--The term "annual percentage yield" means the total amount of interest that would be received on a $100 deposit, based on the annual rate of simple interest and the frequency of compounding for a 365-day period, expressed as a percentage calculated by a method which shall be prescribed by the Board in regulations.[2]
The calculation method is defined as:
![APY = 100 \left [ \left(1 + \frac {Interest} {Principal} \right)^{365 / Days~in~term} - 1 \right ]](http://wpcontent.answcdn.com/wikipedia/en/math/a/a/2/aa2c5229404e91bb8c8b446fd1be5800.png)
Algebraically, this is equivalent to:
![Interest = Principal \left [ \left ( \frac {APY} {100} + 1 \right )^{Days~in~term/365} - 1 \right ]](http://wpcontent.answcdn.com/wikipedia/en/math/1/f/0/1f04f9eb7dafbd49ef4ea08cda999ae7.png)
"Principal" is the amount of funds assumed to have been deposited at the beginning of the account.
"Interest" is the total dollar amount of interest earned on the Principal for the term of the account.
"Days in term" is the actual number of days in the term of the account.
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Barron's Banking Dictionary
Dictionary of Banking Terms. Copyright © 2006 by Barron's Educational Series, Inc. All rights reserved.
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Investopedia Financial Dictionary
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Mentioned in
Marginal Efficiency of Capital
(business term)
Truth in Savings
(in banking)
Basis Price
(in banking)
Effective Rate
(in banking)
Truth-In-Savings Act
(insurance term)
» More