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.
APY
5.127%
Daily rate (APR ÷ 365)
0.0137%
Monthly rate (APR ÷ 12)
0.4167%
APR
5%
APR to APY table
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%
Worked example: convert 5% APR to APY
Daily compounding: n = 365, so APY = (1 + 0.05 / 365)365 − 1 = 5.127%.
Monthly compounding: n = 12, so APY = (1 + 0.05 / 12)12 − 1 = 5.116%.
Annual compounding: n = 1, so APY equals the APR, 5.000%.
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.
Frequently asked questions
How do you convert APR to APY?
APY = (1 + APR / n)^n − 1, where n is the number of times interest compounds per year (365 for daily, 12 for monthly).
How do you convert APY back to APR?
APR = n × ((1 + APY)^(1/n) − 1). For example, a 5% APY compounded daily corresponds to an APR of about 4.879%.
How do I turn an annual rate into a daily rate?
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.
What is the difference between APR and APY?
APR is the stated yearly rate without compounding; APY includes compounding, so it shows what you really earn or pay over a year. Use the APR to APY calculator above to see the gap for any rate and frequency.
Why is APY higher than APR?
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.