Annual Percentage Yield
Encyclopedia
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, 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 .
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%.
s 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:
The calculation method is defined as:
Algebraically, this is equivalent to:
"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.
Interest rate
An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...
, based on a compounding
Compound interest
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called 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
Annual percentage rate
The term annual percentage rate , also called nominal APR, and the term effective APR, also called EAR, describe the interest rate for a whole year , rather than just a monthly fee/rate, as applied on a loan, mortgage loan, credit card, etc. It is a finance charge expressed as an annual rate...
(APR) refers to the rate paid to a financial institution by a borrower.
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). 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 .
Equation
One common mathematical definition of APY uses the effective interest rateEffective interest rate
The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.It is used to compare the...
formula, but the precise usage may depend on local laws.
where
is the nominal interest rateNominal interest rate
In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation ; or, for interest rates "as stated" without adjustment for the full effect of compounding...
and
is the number of compounding periods per year.For large N we have, approximately,
where e is the base of natural logarithms
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
(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 institutionFinancial institution
In financial economics, a financial institution is an institution that provides financial services for its clients or members. Probably the most important financial service provided by financial institutions is acting as financial intermediaries...
s in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, the calculation of the APY and the related annual percentage yield earned are regulated by the FDIC
Federal Deposit Insurance Corporation
The Federal Deposit Insurance Corporation is a United States government corporation created by the Glass–Steagall Act of 1933. It provides deposit insurance, which guarantees the safety of deposits in member banks, currently up to $250,000 per depositor per bank. , the FDIC insures deposits at...
Truth in Savings Act
Truth in Savings Act
The Truth in Savings Act is a United States federal law that was passed on December 19, 1991. It was part of the larger Federal Deposit Insurance Corporation Improvement Act of 1991 and is implemented by Regulation DD...
of 1991:
The calculation method is defined as:
Algebraically, this is equivalent to:
"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.