Annual percentage yield

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In finance, 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.

where

i_nom is the nominal interest rate and

N 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%.

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

• FDIC Law, Regulations, and Related Acts - text of the Truth in Savings Act
• Appendix A to Part 230 of TISA (specifically covers calculation of APY).

External links

• APY calculator.

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