Annual Percentage Yield (APY) Calculator
Calculate APY from nominal interest rate and compounding frequency. Compare savings growth, future value, and total interest earned over time.
About
A nominal interest rate advertised by a bank does not reflect actual earnings. Compounding frequency changes the effective return. A 5% rate compounded daily yields more than the same rate compounded annually. The difference compounds over time and can amount to hundreds or thousands of dollars on large deposits. Failing to compare APY across products means leaving money on the table. This calculator converts any nominal rate and compounding schedule into the standardized Annual Percentage Yield (APY), computed as APY = (1 + rn)n − 1, following the Federal Truth in Savings Act (Regulation DD) methodology.
The tool assumes a fixed nominal rate over the entire period. It does not account for variable-rate products, fees, or early withdrawal penalties. For tiered-rate accounts, calculate each tier separately. Pro tip: always compare APY rather than nominal rate when evaluating certificates of deposit or high-yield savings accounts - it is the only apples-to-apples metric.
Formulas
The Annual Percentage Yield represents the real rate of return on a deposit after accounting for the effect of compounding within a year.
Where r = nominal annual interest rate (as a decimal), and n = number of compounding periods per year.
For continuous compounding, the limit as n → ∞ yields:
Future value of a deposit over t years:
Total interest earned:
Where P = initial principal (deposit amount), t = number of years, FV = future value, and I = total interest earned. The constant e ≈ 2.71828 is Euler's number.
Reference Data
| Nominal Rate | Compounded Annually | Compounded Quarterly | Compounded Monthly | Compounded Daily | Compounded Continuously |
|---|---|---|---|---|---|
| 1.00% | 1.0000% | 1.0038% | 1.0046% | 1.0050% | 1.0050% |
| 2.00% | 2.0000% | 2.0151% | 2.0184% | 2.0201% | 2.0201% |
| 3.00% | 3.0000% | 3.0339% | 3.0416% | 3.0453% | 3.0455% |
| 4.00% | 4.0000% | 4.0604% | 4.0742% | 4.0808% | 4.0811% |
| 5.00% | 5.0000% | 5.0945% | 5.1162% | 5.1267% | 5.1271% |
| 6.00% | 6.0000% | 6.1364% | 6.1678% | 6.1831% | 6.1837% |
| 7.00% | 7.0000% | 7.1859% | 7.2290% | 7.2501% | 7.2508% |
| 8.00% | 8.0000% | 8.2432% | 8.3000% | 8.3278% | 8.3287% |
| 9.00% | 9.0000% | 9.3083% | 9.3807% | 9.4162% | 9.4174% |
| 10.00% | 10.0000% | 10.3813% | 10.4713% | 10.5156% | 10.5171% |
| 12.00% | 12.0000% | 12.5509% | 12.6825% | 12.7475% | 12.7497% |
| 15.00% | 15.0000% | 15.8650% | 16.0755% | 16.1798% | 16.1834% |
| 18.00% | 18.0000% | 19.2519% | 19.5618% | 19.7164% | 19.7217% |
| 20.00% | 20.0000% | 21.5506% | 21.9391% | 22.1336% | 22.1403% |
| 25.00% | 25.0000% | 27.4429% | 28.0732% | 28.3916% | 28.4025% |