APY Calculator
By Alastair Hazell.
Reviewed by Chris Hindle.
Use the APY calculator to work out the total interest and annual compounded interest rate on your investment or savings.
Disclaimer: Whilst every effort has been made in building our calculator tools, we are not to be held liable for any damages or monetary losses arising out of or in connection with their use. Full disclaimer.
What is APY?
APY stands for ‘annual percentage yield’, sometimes known as ‘annual interest yield' or the ‘effective annual rate’. It is a metric that reflects the total return or earnings on your investment or savings account over the course of one year.
APY takes into account the impact of compounding, which means that it considers the interest earned on both the initial Principal and any accumulated interest. It is a standardized measure that allows for easy comparison between different financial products or accounts.
APY represents the effective rate of return for a 365-day period and provides a more accurate representation of the actual interest earned, considering the frequency of compounding and the investment duration. It is a valuable tool for consumers to assess and compare the potential growth of investments or the returns on savings accounts. 1
Keep scrolling to see how the APY formula works, together with some example calculations...
How to calculate APY from APR
To calculate APY based upon a nominal APR, raise the sum of one plus the annual interest rate (APR) (expressed as a decimal) divided by the number of compounding periods to the power of the number of compounding periods. Then, subtract one from the result.
This APY figure represents the total effective interest earned on the investment over a year, accounting for compounding.
The APY formula looks like this:
Where:
- r = nominal APR (as decimal)
- n = the number of times interest is compounded per year (e.g. 12 for monthly, or 4 for quarterly)
Example
As a simple example, let's say you are receiving a nominal APR of 6% on your investment, with monthly compounding (12 compounds per year). Feeding these into our formula, r = 0.06 (APR as decimal) and n = 12:
- APY = (1 + r/n)^n – 1
- APY = (1 + 0.06/12)^12 – 1
- APY = (1 + 0.005)^12 – 1
- APY = 1.005^12 – 1
- APY = 1.06167781186 – 1
- APY = 0.06167781186
Our decimal APY is 0.06167. To transform the figure into a percentage, we multiply it by 100. Doing so gives us a figure of 6.17%. We can see that our calculation is correct when we check the figure against our APY calculator (at the top of the page).
See also: Compound Interest | Simple Interest | Savings Calculator
How to calculate APY from Principal and interest earned
To calculate APY based on the interest earned on a Principal sum, you can use the following general formula: 2
Example
In this example, we'll say that you earn $50 interest on a $1,000 investment over the course of one year (365 'days in term').
Plugging these figures into the formula, we can calculate as follows:
- APY = 100 × [(1 + 50 / 1000)^(365/365) - 1]
- APY = 100 × [(1 + 0.05)^(1) - 1]
- APY = 100 × [1.05 - 1]
- APY = 5
The APY on the above example is 5%. Checking this figure against our interest rate calculator confirms that our calculation is correct.
How to calculate interest from APY and Principal
To calculate the amount of interest earned on an investment with a set APY, we can use the following formula:
In this formula, "Principal" represents the initial amount invested, and "APY" represents the Annual Percentage Yield expressed as a percentage.
To calculate the interest, divide the APY by 100 to convert it to a decimal, then multiply it by the Principal amount. Let's try another example...
Example
Let's say you're looking to find out what interest you will receive on an investment of $1,000 at 5% APY. Here's how to calculate it:
- Interest = Principal × (APY/100)
- Interest = 1000 × (5/100)
- Interest = 1000 × 0.05
- Interest = $50
The interest earned on $1,000 at 5% APY is $50.
What is the difference between APY and APR?
The nominal APR (annual percentage rate) is also called the base rate of a product. It’s the basic, advertised-everywhere, not-including-compounding, number-on-the-tin rate. The APY rate is the figure that includes compounding. You can enter either within our calculator (indeed, our APY calculator will work out the APY rate for you, if you enter the APR/nominal rate).
Example
Let's illustrate the difference between Annual Percentage Rate (APR) and Annual Percentage Yield (APY) with a practical example.
We'll suppose you're comparing two investment options: Investment A offers an APR of 5%, compounded semi-annually, while Investment B offers an APR of 5%, compounded monthly.
We can calculate the APY for each account, using the main APY formula we discussed earlier: APY = (1 + r/n)n – 1
- For Investment A: APY = (1 + 0.05/2)^2 - 1 = 5.0625%.
- For Investment B: APY = (1 + 0.05/12)^12 - 1 = 5.1164%.
In this example, both Investment A and Investment B have the same APR of 5%. As we can see, however, due to the different compounding frequencies, Investment B with monthly compounding offers a slightly higher APY compared to Investment A with semi-annual compounding.
On a $10,000 investment over one year, Investment B would accumulate $511.62 of yearly interest, compared to $506.25 for Investment A.
This example emphasizes how even a slight variation in compounding frequencies can result in a small difference in APY, showcasing the impact of compounding on investment returns. Higher compounding frequencies, such as monthly compounding, can lead to slightly higher APYs and potentially provide a marginally greater overall return over time, compared to less frequent compounding.
You can learn more about the different types of interest rates, including effective rates and APR, in our article about interest rate types here. And, you can scroll back up to our calculator here.
Thanks for reading
I hope you found our APR calculator and explanations helpful. If you did, you may wish to browse through our selection of other useful finance calculators, including our handy interest rate calculator.
As always, it is advisable to seek guidance from a professional financial advisor before making any significant financial decisions. Their expertise can provide valuable insights and help you make informed choices that align with your individual financial goals and circumstances.
References
- 1030.2 Definitions, Consumer Finance Protection Bureau (CFPB).
- Appendix A, Part I. Annual Percentage Yield for Account Disclosures and Advertising Purposes, Consumer Finance Protection Bureau (CFPB).