APR to APY Converter
The stated annual interest rate (without compounding)
How often interest is compounded and reinvested
APR vs APY
APR (Annual Percentage Rate):
The simple annual interest rate without accounting for compounding.
APY (Annual Percentage Yield):
The effective annual return when compounding is included. APY is always ≥ APR.
Formula
Standard Compounding:
APY = (1 + APR/n)n - 1Where n = number of compounds per year
Continuous Compounding:
APY = eAPR - 1Examples
• 10% APR, yearly compounding → 10.00% APY
• 10% APR, monthly compounding → 10.47% APY
• 10% APR, daily compounding → 10.52% APY
• 10% APR, continuous compounding → 10.52% APY (max)
Crypto Context
• DeFi Protocols: Often quote APY (includes auto-compounding)
• CEX Staking: May quote APR (manual claim & restake)
• Liquidity Mining: APR if you manually compound, APY if auto-compound
• More frequent compounding = higher APY from same APR
Convert an annual percentage rate (APR) into the annual percentage yield (APY) it produces with daily, weekly, monthly, quarterly, yearly or continuous compounding, to compare savings accounts, CDs and loans on the same footing.
Formula
Worked Example
Monthly compounding pays 5% ÷ 12 = 0.4167% a month, and (1.004167)¹² − 1 = 5.1162%. With daily compounding the same APR gives 5.1267%, and the continuous maximum is 5.1271%.
Frequently Asked Questions
What is the difference between APR and APY?
APR is the annual rate before compounding; APY is what you actually earn or pay in a year once interest earns interest. Banks advertise APY on savings because it is higher, and lenders quote APR on loans. For the same APR, more frequent compounding means a higher APY.
Why does my credit card's APR understate what I pay?
Card interest is usually charged on the average daily balance at APR ÷ 365 per day, which compounds monthly when the interest is added to the balance. A 24% APR carried for a year costs about 26.8%.
How do I convert APY back to APR?
APR = n × ((1 + APY)^(1/n) − 1). A 5% APY with monthly compounding corresponds to an APR of 12 × (1.05^(1/12) − 1) = 4.889%.