APR to APY Calculator

What is APR to APY Conversion?

The APR to APY Calculator converts Annual Percentage Rate (APR) to Annual Percentage Yield (APY), accounting for the powerful effect of compound interest. While APR represents the simple annual interest rate without compounding, APY reflects the actual rate of return you earn (or pay) over a year, considering how often interest is compounded. Understanding this difference is crucial for making informed financial decisions about savings accounts, loans, credit cards, and investments.

For example, a savings account with a 5% APR that compounds monthly actually yields about 5.12% APY. This means on a $10,000 deposit, you earn $512 instead of $500 over one year. The difference becomes even more significant over longer periods. This free APR to APY Converter helps you quickly determine the true yield for any combination of rate and compounding frequency.

The APR to APY Formula

The conversion from APR to APY follows a simple mathematical formula:

Where:

• APR is the Annual Percentage Rate (expressed as a decimal)
• n is the number of compounding periods per year

For continuous compounding, the formula uses Euler's number $e$:

Continuous compounding represents the theoretical maximum APY achievable for a given APR. While no real financial product offers true continuous compounding, daily compounding closely approaches this limit. Our APR to APY Calculator supports all standard compounding frequencies including annual, semi-annual, quarterly, monthly, daily, and continuous.

Why APY Matters More Than APR

When comparing financial products, APY gives you a more accurate picture of true earnings or costs. Two accounts may advertise the same APR but have different APYs due to different compounding frequencies. For instance, a credit card with 24% APR compounded monthly has an effective APY of 26.82%, meaning you actually pay nearly 27% interest if you carry a balance. Our Annual Percentage Yield Calculator reveals these important differences instantly.

For more financial calculations, explore our Compound Interest Calculator and Continuous Compounding Calculator.

Common Compounding Frequency Comparison

The table below shows how different compounding frequencies affect the APY for a 5% APR:

• Annual: 5.000% APY (same as APR)
• Semi-annual: 5.062% APY
• Quarterly: 5.095% APY
• Monthly: 5.116% APY
• Daily: 5.127% APY
• Continuous: 5.127% APY (theoretical maximum)

As you can see, the difference between monthly and daily compounding is relatively small, while the jump from annual to semi-annual compounding provides the most significant increase.