About the APR to APY Calculator
Banks advertise savings accounts and CDs with an APY and loans and credit cards with an APR. The difference is compounding: an APR is the nominal yearly rate, while the APY (also called the effective annual rate, EAR) includes interest earned on interest. This calculator converts APR to APY and APY to APR for annual, semiannual, quarterly, monthly, weekly, daily and continuous compounding, and converts annual rates to monthly rates and back.
How to use
- Choose APR → APY, enter the APR and pick how often interest compounds.
- Read the APY and the formula with your numbers; the table compares every compounding frequency.
- To find which APR gives a target APY, switch to APY → APR.
- Use the bottom card to convert an annual rate to a monthly rate, or a monthly rate to an annual rate.
APR and APY formulas
| Conversion | Formula |
|---|---|
| APR → APY | (1 + APR ÷ n)n − 1 |
| Continuous | eAPR − 1 |
| APY → APR | n × ((1 + APY)1/n − 1) |
| Annual → monthly (compound) | (1 + annual)1/12 − 1 |
| Monthly → annual (compound) | (1 + monthly)12 − 1 |
n is the number of compounding periods per year. Example: 5% APR compounded monthly is (1 + 0.05/12)12 − 1 = 5.1162% APY; daily compounding gives 5.1267% and continuous 5.1271%.
APR vs APY: what’s the difference?
- APR (annual percentage rate) is the yearly rate without compounding. For loans, the Truth in Lending Act APR also includes certain fees, so it can be higher than the note rate.
- APY (annual percentage yield) is what a deposit actually earns in a year with compounding. Under the Truth in Savings Act (Regulation DD) US banks must disclose APY on deposit accounts.
- When saving, compare accounts by APY. When borrowing, the effective rate is what you really pay: a credit card with 22% APR compounded daily costs about 24.60% a year if the balance is carried.
Converting annual and monthly rates
Lenders divide the APR by 12 to get the monthly rate (6% APR → 0.5% a month). Going the other way, 1% a month is a 12% APR, but if it compounds the balance grows by (1.01)12 − 1 = 12.68% a year. For investment returns that compound, use the compound conversion.
FAQ
What is the APY of 5% APR compounded monthly?
(1 + 0.05 ÷ 12)^12 − 1 = 5.1162%. $10,000 grows to $10,511.62 in one year.
What is the real annual rate of a 22% credit card APR?
Credit cards usually compound daily, so a 22% APR is about 24.60% effective per year (24.36% if compounded monthly).
How do I convert APY to APR?
Choose APY → APR and enter the APY. With monthly compounding, APR = 12 × ((1 + APY)^(1/12) − 1); a 5% APY corresponds to a 4.8889% APR.
What is continuous compounding?
The limit when interest compounds infinitely often: APY = e^APR − 1. It is used in finance and option pricing; for a 5% APR it gives 5.1271%.