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 is the nominal yearly rate before compounding; APY is the effective rate after compounding. A 5% APR compounded monthly is a 5.1162% APY. With annual compounding the two are identical.
Why do banks quote APY on savings but APR on loans?
Each figure flatters the product. APY is the bigger number, so it makes deposits look better; APR ignores intra-year compounding, so it makes loans look cheaper. US rules also require APY on deposit disclosures and APR on credit disclosures.
Does compounding frequency matter much?
Honestly, not a lot at consumer rates. On $10,000 at 5% APR, monthly compounding beats annual by about $11.62 a year, and daily adds only about $1.05 over monthly. Compare APYs, not frequencies.
How do I convert APY back to APR?
APR = n x ((1 + APY)^(1/n) - 1) for n compounding periods, or ln(1 + APY) for continuous compounding. A 5.1162% APY with monthly compounding converts back to exactly 5.00% APR.
Is this APY calculator free?
Yes. Free, no sign-up, and every calculation runs locally in your browser. Nothing you type is uploaded.