Example of Annual Percentage Yield

Definition

Annual Percentage Yield (APY) is a measure of the total amount of interest paid on a deposit account over a year, taking into account the effect of compounding, as first described by economist Eugen von Böhm-Bawerk in his work on interest theory.

How It Works

The APY is calculated by considering the nominal interest rate, which is the stated interest rate, and the compounding frequency, which determines how often the interest is added to the principal. For instance, if a savings account has a nominal interest rate of 2% and compounds annually, the APY will be 2.02% if it compounds monthly, due to the effect of compounding, as explained by Fisher's equation of exchange. The APY formula is: APY = (1 + r/n)^(n) - 1, where r is the nominal interest rate and n is the number of compounding periods per year.

The APY is affected by the Federal Reserve's monetary policy, which influences the overall level of interest rates in the economy. For example, when the Federal Reserve lowers the federal funds rate, banks and other financial institutions often reduce their deposit rates, leading to lower APYs on savings accounts. Conversely, when the Federal Reserve raises the federal funds rate, deposit rates tend to increase, resulting in higher APYs. According to data from the Federal Deposit Insurance Corporation (FDIC), the average APY on a one-year certificate of deposit (CD) was around 2.5% in 2020.

Key Components

• Compounding frequency: determines how often the interest is added to the principal, with more frequent compounding resulting in higher APYs. For example, an account with a nominal interest rate of 2% and daily compounding will have a higher APY than one with annual compounding.
• Nominal interest rate: the stated interest rate, which serves as the basis for calculating the APY. A higher nominal interest rate will result in a higher APY, assuming the compounding frequency remains the same.
• Principal amount: the initial deposit amount, which affects the total interest earned and the APY. A larger principal amount will result in more interest earned, but the APY remains the same.
• Time: the length of time the money is deposited, with longer periods resulting in more interest earned and a higher APY. For instance, a five-year CD will typically have a higher APY than a one-year CD.
• Interest rate risk: the risk that changes in interest rates will affect the APY, with rising interest rates benefiting depositors and falling interest rates benefiting borrowers. According to Milton Friedman's theory of interest rates, changes in interest rates can have significant effects on the overall economy.
• Liquidity: the ability to access the deposited funds, with more liquid accounts often having lower APYs. For example, a checking account may have a lower APY than a savings account or CD, due to its higher liquidity.

Common Misconceptions

Myth: APY is the same as the nominal interest rate — Fact: APY takes into account the effect of compounding, which can result in a higher effective interest rate, as described by Irving Fisher's theory of interest.

Myth: A higher APY always means a better deal — Fact: Other factors, such as fees, liquidity, and interest rate risk, should also be considered when evaluating a deposit account, according to Modigliani-Miller's theory of capital structure.

Myth: APY is only relevant for savings accounts — Fact: APY is also relevant for other types of deposit accounts, such as CDs and money market accounts, as well as for loans and credit cards, which can have APR (Annual Percentage Rate), as explained by Stiglitz's theory of credit markets.

Myth: APY is fixed and does not change over time — Fact: APY can change over time due to changes in interest rates, compounding frequency, or other factors, such as inflation, which can erode the purchasing power of deposited funds, as described by Friedman's theory of inflation.

In Practice

For instance, Bank of America offers a savings account with a nominal interest rate of 1.5% and daily compounding, resulting in an APY of 1.51%. If a depositor puts $10,000 into this account, they will earn approximately $151 in interest over the course of a year, assuming the interest rate remains constant. In contrast, a Wells Fargo CD with a nominal interest rate of 2.5% and annual compounding will have an APY of 2.5%, resulting in $250 in interest earned over a year on a $10,000 deposit. According to data from the FDIC, the average APY on a one-year CD was around 2.5% in 2020, with some banks offering rates as high as 3.5% (Ally Bank).