Enter Interest Rate
Rate Type
Quick Reference
- APR = Annual Percentage Rate (nominal, stated)
- APY = Annual Percentage Yield (effective, actual)
- More frequent compounding = higher effective rate
- Continuous compounding uses er formula
Conversion Result
Equivalent Rates
Nominal (APR)| Compounding Frequency | Nominal Rate (APR) | Copy |
|---|---|---|
| Daily (365/year) | -- | |
| Weekly (52/year) | -- | |
| Monthly (12/year) | -- | |
| Quarterly (4/year) | -- | |
| Semi-Annually (2/year) | -- | |
| Annually (1/year) | -- | |
| Continuous (er) | -- |
Key Insight
Enter an interest rate above to see how it converts across different compounding frequencies. The more frequently interest compounds, the higher the effective annual yield.
Understanding Interest Rate Conversions
APR vs APY: What's the Difference?
APR (Annual Percentage Rate) is the nominal or stated interest rate. It's the rate before considering the effects of compounding. Lenders often advertise APR because it appears lower than the actual cost of borrowing.
APY (Annual Percentage Yield), also called EAR (Effective Annual Rate), is the actual return you earn (or pay) after compounding is factored in. Banks advertise APY on savings accounts because it looks higher than the nominal rate.
How Compounding Frequency Affects Returns
The more frequently interest compounds, the higher your effective return. Consider a 10% annual rate:
- Annually: 10.00% APY (no compounding within the year)
- Quarterly: 10.38% APY
- Monthly: 10.47% APY
- Daily: 10.52% APY
- Continuous: 10.52% APY (mathematical limit)
The Formulas
Where n is the number of compounding periods per year, and e is Euler's number (≈ 2.71828).
Continuous Compounding Explained
Continuous compounding is the mathematical limit of compounding—interest is calculated and added instantaneously at every moment. While no real-world investment compounds continuously, this concept is crucial in:
- Options pricing: The Black-Scholes model uses continuous compounding
- Theoretical finance: Simplifies many mathematical derivations
- Benchmark comparisons: Provides a consistent standard for comparing rates
Practical Applications
Understanding interest rate conversions is essential for:
- Comparing savings accounts: Banks quote APY, but compounding frequency varies
- Evaluating loans: Lenders advertise APR, but actual cost depends on compounding
- Investment analysis: Convert rates to a common basis for fair comparison
- Financial modeling: Ensure consistency when combining rates from different sources
Frequently Asked Questions
Important Disclaimer
This calculator is for educational purposes only. Results are based on mathematical formulas and may not account for fees, taxes, or other factors that affect actual returns. Always verify calculations with your financial institution. This is not financial advice.
