APY Calculator
Convert APR to APY or APY to APR at any compounding frequency, and see how much one year of interest actually adds to your balance.
| If compounded | APY |
|---|
Interest figures assume no deposits, withdrawals or fees for the year, and the rate staying constant. Rates shown to 4 decimals so small compounding differences stay visible.
APR to APY formula
For a nominal rate r compounded n times per year, the effective annual yield is APY = (1 + r/n)^n - 1. A 5% APR compounded monthly becomes (1 + 0.05/12)^12 - 1 = 5.1162%. With continuous compounding the formula becomes APY = e^r - 1, giving 5.1271% at the same 5% nominal rate. To go the other way, APR = n x ((1 + APY)^(1/n) - 1), or ln(1 + APY) for continuous compounding.
How much does compounding frequency matter?
| 5% APR compounded | APY | Interest on $10,000 after 1 year |
|---|---|---|
| Annually | 5.0000% | $500.00 |
| Semiannually | 5.0625% | $506.25 |
| Quarterly | 5.0945% | $509.45 |
| Monthly | 5.1162% | $511.62 |
| Daily | 5.1267% | $512.67 |
| Continuously | 5.1271% | $512.71 |
The full spread from annual to continuous compounding is about $12.71 a year on $10,000 at 5%. Most of that gain is captured by monthly compounding, and daily adds barely a dollar more. When comparing savings accounts, the APY already folds frequency in, so a higher APY always wins regardless of the quoted schedule.
Frequently asked questions
What is the difference between APY and APR?
APR (annual percentage rate) is the nominal yearly rate before compounding. APY (annual percentage yield) is the effective yearly rate after compounding is included. At 5% APR compounded monthly, the APY is 5.1162%, because each month the interest itself starts earning interest. When interest compounds once a year, APR and APY are identical.
Why do banks quote APY on savings but APR on loans?
Because each number flatters the product being sold. APY is always equal to or higher than the APR for the same account, so quoting APY makes a savings account look more generous. On loans, US lenders must disclose APR, which ignores intra-year compounding and therefore looks smaller than the effective cost. Regulation also drives this: the Truth in Savings Act requires APY on deposit disclosures, while the Truth in Lending Act requires APR on credit.
Does compounding frequency matter much?
Less than most people expect at consumer rates. On a 5% APR, moving from annual to monthly compounding raises the yield from 5.0000% to 5.1162%, worth about $11.62 extra per year on a $10,000 balance. Going from monthly to daily adds only about $1.05 more. The rate itself matters far more than the frequency, so compare APY across accounts rather than the compounding schedule.
How do I convert APY back to APR?
Invert the compounding formula. For n compounding periods per year, APR = n x ((1 + APY)^(1/n) - 1). For example, an APY of 5.1162% with monthly compounding gives APR = 12 x (1.051162^(1/12) - 1) = 5.00%. For continuous compounding, APR = ln(1 + APY). Switch this calculator to APY to APR mode to do it automatically.
Is this APY calculator free?
Yes. It is completely free, requires no sign-up, and all calculations run locally in your browser. Nothing you type is uploaded anywhere.