How to Calculate an Annual Percentage Rate (APY)

Knowing how to calculate Annual Percentage Yield, also referred to with the acronym APY, can help you with financial transactions such as loan applications. It can do so because it will give you a more accurate measure of how much the loan will cost in contrast to Annual Percentage Rate or APR. This article will illustrate how to calculate annual percentage yield (APY). The first method of calculation is the manual calculation which assists in understanding the reasoning behind annual percentage yield.  

How to calculate APY manually

Knowing how to calculate APY by hand can also be useful in order to understand the mathematical concepts behind the number. The APY formula is commonly known as (1+r/n) (exponent n)-1. This formula may look like another language so thinking of it as financial shorthand might be helpful.

To illustrate further, the APY formula abbreviates the math which involves adding 1 to the nominal interest rate (r) which is first divided by the number of periods (n) for which the investment is compounded. This number is then multiplied by the number of compounded periods after that number is lessened by 1.

Example APY calculation

To illustrate how to calculate APY by hand imagine Mr. Johnson walks into a bank with $1000. He wants to know how much his interest rate will be after it compounds at a nominal interest rate. In other words, the banker tells Mr. Johnson he will received 5% on his investment which is compounded monthly. This 5% is not the APY but rather the annual percentage rate (APR). Mr. Johnson likes to his math by hand to ensure he's not being duped so he pulls out a pencil, calculator and pencil and starts calculating the APR. This is what he writes down:

• Normal interest i.e. Annual Percentage Rate: 5% (r)
• Investment amount: $1000.00
• Time compounded: 1 year
• Compounding periods: Monthly i.e. 12 (n)

APY formula: (1+r/n) (exponent n)-1
(1+.05/12) (exponent 12) -1
= (1+.004.6) to the power of 12 - 1
= 1.051078 - 1
APY = .051078% or 5.11% rounded up

Mr. Johnson now knows his annual percentage yield will be 5.11% with an APR of 5%. It can be a good idea to keep in mind this 5.11% is neither adjusted for inflation nor includes fees. To adjust for inflation the APY would simply subtract the percentage of annual inflation from 5.11%. For example, if inflation is 1.5%, 5.11%- 1.5%=3.61% so Mr. Johnson's real annual percentage rate is now 3.61%.

What about bank fees though? Bank fees can be deducted as a percent of total interest paid at the APY before adjusting for inflation. For example, if management fees for Mr. Johnson's $1000 investment are $10, this is equal to 1% of the total initial investment. Since the real APY is 3.61%, the effective real APY is now 2.61%. In other words, Mr. Johnson will earn 2.61% on his $1000 even though the banker tells him he will earn 5%.

Using a calculator to calculate APY

A quick way to calculate APY is to use a bankrate.com or other APY calculator. This is because the formulas for the online application are already programmed and entered and no lengthy hand calculations are needed. Other ways to calculate Annual Percentage Yield (APY) are either use a mathematical formula with a calculator, or by using software applications such as Microsoft Excel.

All that is required for calculating APY with an online calculator is the entering of the key variables, these variables are (1) nominal i.e. non-adjusted, non-compounded base interest rate, (2) the number of periods for which compounding will take place, (3) the investment amount and (4) and the frequency of compounding. Annual percentage yield will provide an accurate interest rate on an investment before fees and inflation.

Distinguishing between APY, EAR and APR

When calculating annual percentage yield (APY) it is important to distinguish it from annual percentage rate (APR), Effective Annual Rate (EAR) and effective annual percentage yield (EAPY).  EAR and APY are the same but are applied to different scenarios i.e. borrowing Vs lending within the banking industry. Effective annual percentage yield can be thought of as the APY with any extra costs such as fees and inflation incorporated into the formula.

APR does not include compounding which APY does and APY does not include fees or inflation in its calculation. In other words, knowing how to calculate APY is one way to be more aware of interest, however is not necessarily the true amount of value earned on an investment. When investing or borrowing it is more accurate to know the APY and therefore more representative on any gains or costs associated with financial instruments such as mortgages, certificates of deposit and savings accounts.

Source: http://www.fdic.gov (Federal Deposit Insurance Corporation)