APY is the rate you actually earn in a year once interest compounds; APR is the rate before compounding. Convert one into the other for daily, monthly, quarterly or annual compounding, and see the matching daily and monthly interest rates.
| APR | APY, daily | APY, monthly | APY, quarterly |
|---|---|---|---|
| 1% | 1.005% | 1.005% | 1.004% |
| 2% | 2.02% | 2.018% | 2.015% |
| 3% | 3.045% | 3.042% | 3.034% |
| 4% | 4.081% | 4.074% | 4.06% |
| 5% | 5.127% | 5.116% | 5.095% |
| 6% | 6.183% | 6.168% | 6.136% |
| 8% | 8.328% | 8.3% | 8.243% |
| 10% | 10.516% | 10.471% | 10.381% |
APY = (1 + APR / n)n − 1 and APR = n × ((1 + APY)1/n − 1), with n = 365 for daily, 12 for monthly, 4 for quarterly and 1 for annual compounding.
APY = (1 + APR / n)^n − 1, where n is the number of times interest compounds per year (365 for daily, 12 for monthly).
APR = n × ((1 + APY)^(1/n) − 1). For example, a 5% APY compounded daily corresponds to an APR of about 4.879%.
Divide the APR by 365: a 5% APR is about 0.0137% a day. If you start from APY, the equivalent daily growth rate is (1 + APY)^(1/365) − 1.
Because interest earned during the year starts earning interest too. The more often it compounds, the bigger the gap, though daily and monthly compounding differ only a little.