APY Calculator: Nominal Rate to Effective Annual Yield (2026)
Annual Percentage Yield (APY) reveals what a rate really pays once compounding is counted. Enter a nominal rate and see the effective annual return at every compounding frequency — the gap between the headline number and your true yield.
Quick answer: APY = (1 + Nominal% ÷ n)n − 1, where n is how many times interest compounds per year. A 5% nominal rate compounded monthly is about 5.12% APY; compounded daily it is about 5.13% APY.
APY Calculator
Monthly compounding APY
5.116%
n = 12
Daily compounding APY
5.127%
n = 365
| Compounding | Periods / Year (n) | APY | vs Nominal |
|---|---|---|---|
| Annually | 1 | 5.000% | +0.000 pts |
| Semiannually | 2 | 5.062% | +0.062 pts |
| Quarterly | 4 | 5.095% | +0.095 pts |
| Monthly | 12 | 5.116% | +0.116 pts |
| Daily | 365 | 5.127% | +0.127 pts |
APY rises with compounding frequency. The upper bound is continuous compounding (e^(Nominal%) − 1). All values computed in-page; no external rate is assumed.
APY by Nominal Rate (Monthly Compounding)
| Nominal Rate | Monthly APY | Daily APY |
|---|---|---|
| 1% | 1.005% | 1.005% |
| 2% | 2.018% | 2.020% |
| 3% | 3.042% | 3.045% |
| 4% | 4.074% | 4.081% |
| 5% | 5.116% | 5.127% |
| 6% | 6.168% | 6.183% |
| 7% | 7.229% | 7.250% |
| 8% | 8.300% | 8.328% |
Reference table for monthly and daily compounding. Daily APY is marginally higher because interest is credited more often. Values are exact closed-form results.
Nominal Rate vs APY
A bank may advertise a 5% interest rate, but if that rate compounds monthly, you do not earn 5% on your original balance for the whole year — you earn 5% on a slightly larger balance each month as prior interest is added. That snowball pushes the effective yearly return above the stated number. APY is the standardized way to compare accounts: it always assumes reinvestment and a one-year horizon.
The formula is the closed-form solution of compounding: APY = (1 + Nominal% ÷ n)n − 1. As n grows, APY approaches the continuous limit e^(Nominal%) − 1. At typical savings rates the difference between monthly and daily compounding is tiny, but it matters more at higher rates and over longer horizons.
Sources & Methodology
- APY / effective annual rate formula: standard compound-interest mathematics (closed-form solution of periodic compounding over one year). Source: foundational finance/algebra reference; retrieval August 2026.
- All values computed in-page with JavaScript:
(1 + nominal/100/n)^n − 1. No external or “current” market rate is assumed, so the table does not go stale. - For related growth math, see the Rule of 72 table and the CAGR calculator.
Related Calculators & Guides
The CompoundFig Editorial Team · Independent Editorial Research Project
Reviewed by The CompoundFig Editorial Team, Editorial Review.