APY to APR Calculator
Free APY to APR converter and APR to APY calculator. Convert between Annual Percentage Yield and Annual Percentage Rate with daily, monthly, or continuous compounding.
Understanding APY vs APR
APR (Annual Percentage Rate) is the simple interest rate stated on an annual basis. It does not account for compounding effects. APR is typically used for loans and credit cards to represent the nominal interest rate plus any fees or additional costs.
When you see an APR advertised, it represents the yearly cost of funds over the term of a loan or credit card balance, including fees and costs related to the transaction.
APY (Annual Percentage Yield) is the effective annual rate of return taking into account the effect of compounding interest. APY is typically used for investment products and savings accounts.
APY provides a more accurate representation of the actual return on investment or the true cost of borrowing when interest compounds more frequently than annually.
Converting between APR and APY allows you to:
- Compare different financial products on an equal basis
- Understand the true cost of borrowing or return on investment
- Make more informed financial decisions
- See how compounding frequency affects your interest
Financial institutions may advertise whichever rate makes their product look more attractive. Lenders typically advertise loans using APR (which appears lower) while savings accounts are advertised with APY (which appears higher).
The frequency of compounding has a significant impact on the difference between APR and APY. The more frequently interest compounds, the greater the difference between the two rates.
Common compounding frequencies include:
- Annually: Once per year
- Semi-annually: Twice per year
- Quarterly: Four times per year
- Monthly: 12 times per year
- Weekly: 52 times per year
- Daily: 365 times per year
- Continuous: Infinite compounding
APY to APR Conversion Formulas
Use these formulas to manually convert APY to APR or convert APR to APY with any compounding frequency.
How to Convert APR to APY
APY = (1 + APR/n)^n - 1
Where n is the number of compounding periods per year (12 for monthly, 365 for daily compounding).
How to Convert APY to APR
APR = n × ((1 + APY)^(1/n) - 1)
Where n is the number of compounding periods per year. Use our APY to APR converter above for instant calculations.
Continuous Compounding Formula
APY = e^APR - 1
For continuous compounding, the APR to APY conversion uses the mathematical constant e (≈2.71828). This represents the maximum possible APY for a given APR.
APR to APY Conversion Examples
See how different compounding frequencies affect the APY for common APR values.
| APR | APYMonthly | APYDaily | APYContinuous |
|---|---|---|---|
| 3.00% | 3.04% | 3.05% | 3.05% |
| 5.00% | 5.12% | 5.13% | 5.13% |
| 7.00% | 7.23% | 7.25% | 7.25% |
| 10.00% | 10.47% | 10.52% | 10.52% |
| 15.00% | 16.08% | 16.18% | 16.18% |
| 20.00% | 21.94% | 22.13% | 22.14% |
| 25.00% | 28.07% | 28.39% | 28.40% |