APR and APY Calculator
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Understanding APR and APY: The True Cost and Return of Money
When dealing with loans, savings accounts, or investments, you'll frequently encounter two important terms: Annual Percentage Rate (APR) and Annual Percentage Yield (APY). While they both relate to interest rates, they represent different aspects of how interest is calculated and applied. Understanding the distinction is crucial for making informed financial decisions.
What is Annual Percentage Rate (APR)?
The Annual Percentage Rate (APR) is the annual rate charged for borrowing or earned through an investment, expressed as a percentage. It represents the simple interest rate for a year, without taking into account the effect of compounding interest within that year. For loans, APR includes not only the interest rate but also other fees and costs associated with the loan, giving a more comprehensive picture of the annual cost of borrowing.
For example, if you have a credit card with an APR of 18%, it means you're charged 18% interest over the course of a year on your outstanding balance, assuming no compounding within the year or if interest is only calculated annually.
What is Annual Percentage Yield (APY)?
The Annual Percentage Yield (APY), also known as the Effective Annual Rate (EAR), is the effective annual rate of return taking into account the effect of compounding interest. Compounding means earning interest on your initial principal *and* on the accumulated interest from previous periods. APY provides a more accurate representation of the actual amount of interest earned on an investment or paid on a loan over a year, especially when interest is compounded more frequently than annually.
Because APY accounts for compounding, it will always be equal to or higher than the APR when interest is compounded more than once a year. For savings accounts and investments, a higher APY is better. For loans, a lower APY (or effective rate) is better.
The Key Difference: Compounding
The fundamental difference between APR and APY lies in compounding. APR is a nominal rate, often quoted without considering the frequency of compounding. APY, on the other hand, is an effective rate that explicitly incorporates the impact of compounding.
- If interest is compounded only once a year (annually), then APR = APY.
- If interest is compounded more frequently (e.g., semi-annually, quarterly, monthly, daily), then APY will be higher than APR.
How Compounding Frequency Impacts APY
The more frequently interest is compounded, the higher the APY will be for a given APR. This is because your interest starts earning interest sooner. Let's look at an example using the calculator:
Imagine an investment with an Annual Percentage Rate (APR) of 5%.
- Compounded Annually (n=1):
APY = (1 + (0.05 / 1))^1 – 1 = 0.05 = 5.000%
Here, APR = APY because interest is only compounded once a year. - Compounded Semi-annually (n=2):
APY = (1 + (0.05 / 2))^2 – 1 = (1 + 0.025)^2 – 1 = 1.050625 – 1 = 0.050625 = 5.063% - Compounded Quarterly (n=4):
APY = (1 + (0.05 / 4))^4 – 1 = (1 + 0.0125)^4 – 1 = 1.050945 – 1 = 0.050945 = 5.095% - Compounded Monthly (n=12):
APY = (1 + (0.05 / 12))^12 – 1 = (1 + 0.00416667)^12 – 1 = 1.051162 – 1 = 0.051162 = 5.116% - Compounded Daily (n=365):
APY = (1 + (0.05 / 365))^365 – 1 = (1 + 0.000136986)^365 – 1 = 1.051267 – 1 = 0.051267 = 5.127%
As you can see, even with the same 5% APR, the APY increases as the compounding frequency becomes more frequent. This small difference can add up significantly over time, especially with larger principal amounts or longer investment horizons.
When to Use Which Rate
- For Loans (especially mortgages, car loans): APR is often used to compare the total cost of different loans, as it includes fees. However, for comparing the true interest cost, understanding the effective rate (APY) based on compounding is also valuable.
- For Savings Accounts and Investments (CDs, high-yield savings): APY is the more important figure. It tells you the actual annual return you will earn on your money, taking into account how often the interest is added to your balance. Always look for the highest APY when saving or investing.
Use our APR and APY calculator to quickly see how different compounding frequencies affect the true annual yield of an investment or the effective cost of a loan. Simply input the Annual Percentage Rate and select the compounding frequency to get the corresponding APY.