APR to APY Calculator

Use this APR to APY (and APY to APR) calculator to calculate and compare the interest rates compounded at different frequencies: daily, weekly, biweekly, semimonthly, monthly, quarterly, semiannually and annually. The breakdown table provides a direct comparison of the rates compounded on different frequencies. Share the computation with the link generated.

Differences between APR and APY

APR, or Annual Percentage Rate, and APY, or Annual Percentage Yield, are standardized measures used to express interest rates on an annual basis. However, they differ significantly in their calculation methods and applications. Understanding these differences is essential for anyone looking to make informed financial choices and before delving into the distinctions, let's explore their definitions and applications.

APR: Annual Percentage Rate

APR stands for Annual Percentage Rate and it is the annual rate of return or cost, expressed as a percentage, based on simple interest without factoring in compounding.

The term is commonly used to give a projection for loans and borrowing costs, but also applicable to basic investment yields.

APY: Annual Percentage Yield

APY stands for Annual Percentage Yield and it is the annual rate of return, expressed as a percentage, that accounts for compound interest.

The term is primarily used for deposit accounts and investment returns.

APR vs APY

The most significant difference between APR and APY is how they treat compound interest. APY will always be higher than APR for the same nominal interest rate due to the compounding effect. This difference becomes more pronounced with higher interest rates and more frequent compounding periods.

Understandably, with the exclusion of compounding in APR, it is generally preferred by lenders for loans, as it appears lower than the equivalent APY. On the flip side, as APY is represented with compounding, they are preferred by banks and investment firms for savings and investments, as it appears higher than the equivalent APR. There are also cases where APR are used in investment products when the compound frequency is either variable or irregular to provide customers a simple rate of return.

Mathematical Dissection

To calculate APR and APY, the mathematical formulas are:

Where:

• 𝑛 = compound frequency

It is apparent that there is a common variable 𝑛 in both of the above formulas and that is the number of times to compound (compound frequency).

Since the formulas are the same - just rearranged, we will focus on the one deriving APY given a known APR (the equation on the right). As 𝑛 increases, the APY also increases, assuming the APR remains constant. This means more frequent compounding leads to a higher effective annual yield. However, while increasing 𝑛 always increases APY, the effect diminishes as 𝑛 gets larger. The difference between daily and continuous compounding, for instance, is often negligible in practice.

This would mean that for borrowers, a higher compound frequency impose higher effective interest costs on loans; for investors, higher compound frequency results in better returns on investments, all else being equal.

Conclusion

While both APR and APY are important financial metrics, they serve different purposes and are most relevant in different contexts. APR is generally more applicable to borrowing scenarios and provides a simpler, though less comprehensive, view of interest rates. APY, on the other hand, offers a more complete picture of returns or costs over time, making it particularly valuable for savings and investment decisions.

Always consider the compound frequency alongside the stated interest rate to get a true picture of the cost or return of a financial product.