Calculator Panel
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Enter your values above and click Calculate.
What This Calculator Does
This calculator converts nominal Annual Percentage Rate (APR) to Annual Percentage Yield (APY), showing the real return on savings or cost of debt after accounting for compound interest.
How to Use This Calculator
Enter the nominal APR (interest rate) and select the compounding frequency (Daily, Weekly, Monthly, Quarterly, Semi-Annually, or Annually). Click Calculate to see the effective APY.
How the Calculation Works
The underlying math engine processes your inputs using exact formulas. This systematic approach ensures professional, institutional-grade calculation precision:
Mathematical Formula
Formula Legend:
- · APR = Annual Percentage Rate (nominal rate).
- · m = Compounding periods per year (e.g., Monthly = 12, Daily = 365, Quarterly = 4).
Practical Example
A savings account offers a nominal interest rate of 5.0% APR compounding monthly:
Step-by-Step Mathematical Walkthrough:
- 1 APR = 5.0% (0.05).
- 2 Compounding periods (m) = 12.
- 3 Calculate: (1 + 0.05 / 12)^12 - 1 = (1.004167)^12 - 1 = 5.116%.
- 4 The Annual Percentage Yield (APY) is exactly 5.12%.
Important Assumptions & Notes
- The interest rate remains constant for a full year.
- The principal balance is not withdrawn during the compounding period.
- A standard year contains 365 days for daily compounding.
Common Mistakes or Considerations
- Comparing savings accounts using APR instead of APY. APY accounts for compounding and represents the true annual growth rate.
- Ignoring compounding frequencies; more frequent compounding results in a higher APY for the same nominal APR.
Frequently Asked Questions
What is the difference between APR and APY?
APR is the nominal, annualized interest rate before compounding is considered. APY is the effective annual rate including the effects of compound interest.
Is APY always higher than APR?
Yes, as long as interest is compounded more than once a year. If compounded annually, APR and APY are exactly equal.
Does credit card debt use APR or APY?
Credit cards quote interest as APR, but interest compound daily, meaning the actual effective annual cost (APY) is slightly higher.
Why does compounding frequency matter?
Frequent compounding (like daily vs. annual) adds accrued interest back to your principal sooner, generating interest on your interest faster.
Can I convert APY back to APR?
Yes, using the inverse formula: APR = m * [ (APY + 1)^(1/m) - 1 ].